Predator–prey interactions between droplets driven by non-reciprocal oil exchange

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.

Self-Timed and Spatially Targeted Delivery of Chemical Cargo by Motile Liquid Crystal

A key challenge underlying the design of miniature machines is encoding materials with time- and space-specific functional behaviors that require little human intervention. Dissipative processes that drive materials beyond equilibrium and evolve continuously with time and location represent one promising strategy to achieve such complex functions. This work reports how internal nonequilibrium states of liquid crystal (LC) emulsion droplets undergoing chemotaxis can be used to time the delivery of a chemical agent to a targeted location. During ballistic motion, hydrodynamic shear forces dominate LC elastic interactions, dispersing microdroplet inclusions (microcargo) within double emulsion droplets. Scale-dependent colloidal forces then hinder the escape of dispersed microcargo from the propelling droplet. Upon arrival at the targeted location, a circulatory flow of diminished strength allows the microcargo to cluster within the LC elastic environment such that hydrodynamic forces grow to exceed colloidal forces and thus trigger the escape of the microcargo. This work illustrates the utility of the approach by using microcargo that initiate polymerization upon release through the outer interface of the carrier droplet. These findings provide a platform that utilizes nonequilibrium strategies to design autonomous spatial and temporal functions into active materials.

Quorum Sensing in Emulsion Droplet Swarms Driven by a Surfactant Competition System

Quorum sensing enables unicellular organisms to probe their population density and perform behavior that exclusively occurs above a critical density. Quorum sensing is established in emulsion droplet swarms that float at a water surface and cluster above a critical density. The design involves competition between 1) a surface tension gradient that is generated upon release of a surfactant from the oil droplets, and thereby drives their mutual repulsion, and 2) the release of a surfactant precursor from the droplets, that forms a strong imine surfactant which suppresses the surface tension gradient and thereby causes droplet clustering upon capillary (Cheerios) attraction. The production of the imine-surfactant depends on the population density of the droplets releasing the precursor so that the clustering only occurs above a critical population density. The pH-dependence of the imine-surfactant formation is exploited to trigger quorum sensing upon a base stimulus: dynamic droplet swarms are generated that cluster and spread upon spatiotemporally varying acid and base conditions. Next, the clustering of two droplet subpopulations is coupled to a chemical reaction that generates a fluorescent signal. It is foreseen that quorum sensing enables control mechanisms in droplet-based systems that display collective responses in contexts of, e.g., sensing, optics, or dynamically controlled droplet-reactors.

Oversaturating Liquid Interfaces with Nanoparticle-Surfactants

Assemblies of nanoparticles at liquid interfaces hold promise as dynamic "active" systems when there are convenient methods to drive the system out of equilibrium via crowding. To this end, we show that oversaturated assemblies of charged nanoparticles can be realized and held in that state with an external electric field. Upon removal of the field, strong interparticle repulsive forces cause a high in-plane electrostatic pressure that is released in an explosive emulsification. We quantify the packing of the assembly as it is driven into the oversaturated state under an applied electric field. Physiochemical conditions substantially affect the intensity of the induced explosive emulsification, underscoring the crucial role of interparticle electrostatic repulsion.

Emergent dynamics due to chemo-hydrodynamic self-interactions in active polymers

The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (e.g. colloids, droplets, microrobots) and understanding their collective dynamics. The design of flexible, freely jointed active assemblies from autonomously powered sub-components remains a challenge. Here, we report freely-jointed active polymers created using self-propelled droplets as monomeric units. Our experiments reveal that the self-shaping chemo-hydrodynamic interactions between the monomeric droplets give rise to an emergent rigidity (the acquisition of a stereotypical asymmetric C-shape) and associated ballistic propulsion of the active polymers. The rigidity and propulsion of the chains vary systematically with their lengths. Using simulations of a minimal model, we establish that the emergent polymer dynamics are a generic consequence of quasi two-dimensional confinement and auto-repulsive trail-mediated chemical interactions between the freely jointed active droplets. Finally, we tune the interplay between the chemical and hydrodynamic fields to experimentally demonstrate oscillatory dynamics of the rigid polymer propulsion. Altogether, our work highlights the possible first steps towards synthetic self-morphic active matter.

Robustness of traveling states in generic nonreciprocal mixtures

Emergent nonreciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit traveling states with no equilibrium counterpart. Using extensive Brownian dynamics simulations, we investigate the existence and stability of such traveling states in a generic nonreciprocal particle system. By varying a broad range of parameters including aggregate state of mixture components, diffusivity, degree of nonreciprocity, effective spatial dimension and density, we determine that traveling states do exist below the predator-prey regime, but nonetheless are only found in a narrow region of the parameter space. Our work also sheds light on the physical mechanisms for the disappearance of traveling states when relevant parameters are being varied, and has implications for a range of nonequilibrium systems including nonreciprocal phase separating mixtures, nonequilibrium pattern formation and predator-prey models.

Kinetic Theory of Motility Induced Phase Separation for Active Brownian Particles

When two active Brownian particles collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann-Enskog-like kinetic theory is built. A linear stability analysis of the homogeneous state predicts a density instability resulting from the effective velocity reduction of tagged particles predicted by the theory.

Phase-separated droplets swim to their dissolution

Biological macromolecules can condense into liquid domains. In cells, these condensates form membraneless organelles that can organize chemical reactions. However, little is known about the physical consequences of chemical activity in and around condensates. Working with model bovine serum albumin (BSA) condensates, we show that droplets swim along chemical gradients. Active BSA droplets loaded with urease swim toward each other. Passive BSA droplets show diverse responses to externally applied gradients of the enzyme's substrate and products. In all these cases, droplets swim toward solvent conditions that favor their dissolution. We call this behavior "dialytaxis", and expect it to be generic, as conditions which favor dissolution typically reduce interfacial tension, whose gradients are well-known to drive droplet motion through the Marangoni effect. These results could potentially suggest alternative physical mechanisms for active transport in living cells, and may enable the design of fluid micro-robots.

Nonreciprocity and odd viscosity in chiral active fluids

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid [Formula: see text], quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modeled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equations for the three variables is analyzed by means of exact moment equations derived from the Fokker-Planck representation, and numerical Brownian dynamics simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to a nonstationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.

Chemotactic particles as strong electrolytes: Debye-Hückel approximation and effective mobility law

We consider a binary mixture of chemically active particles that produce or consume solute molecules and that interact with each other through the long-range concentration fields they generate. We analytically calculate the effective phoretic mobility of these particles when the mixture is submitted to a constant, external concentration gradient, at leading order in the overall concentration. Relying on an analogy with the modeling of strong electrolytes, we show that the effective phoretic mobility decays with the square root of the concentration: our result is, therefore, a nonequilibrium counterpart to the celebrated Kohlrausch and Debye-Hückel-Onsager conductivity laws for electrolytes, which are extended here to particles with long-range nonreciprocal interactions. The effective mobility law we derive reveals the existence of a regime of maximal mobility and could find applications in the description of nanoscale transport phenomena in living cells.

Billiards with Spatial Memory

Many classes of active matter develop spatial memory by encoding information in space. We present a framework based on mathematical billiards, wherein particles remember their past trajectories. Despite its deterministic rules, such a system is strongly nonergodic and exhibits intermittent statistics and complex pattern formation. We show how these features emerge from the dynamic change of topology. Our work illustrates how the dynamics of a single-body system can dramatically change with spatial memory, laying the groundwork to further explore systems with complex memory kernels.

Pair Interactions of Self-Propelled SiO2-Pt Janus Colloids: Chemically Mediated Encounters

Driven by the necessity to achieve a thorough comprehension of the bottom-up fabrication process of functional materials, this experimental study investigates the pairwise interactions or collisions between chemically active SiO2-Pt Janus colloids. These collisions are categorized based on the Janus colloids' orientations before and after they make physical contact. In addition to the hydrodynamic interactions, the Janus colloids are also known to affect each other's chemical field, resulting in chemophoretic interactions, which depend on the degree of surface anisotropy in reactivity of Janus colloid and the solute-surface interaction at play. Our study reveals that these interactions lead to a noticeable decrease in particle speed and changes in orientation that correlate with the contact duration and yield different collision types. Distinct configurations of contact during collisions were found, whose mechanisms and likelihood are found to be dependent primarily on the chemical interactions. Such estimates of collision and their characterization in dilute suspensions shall have a key impact in determining the arrangement and time scales of dynamical structures and assemblies of denser suspensions and potentially the functional materials of the future.

Shaping active matter from crystalline solids to active turbulence

Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.

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.

Reconfigurable Droplet-Droplet Communication Mediated by Photochemical Marangoni Flows

Droplets are attractive building blocks for dynamic matter that organizes into adaptive structures. Communication among collectively operating droplets opens untapped potential in settings that vary from sensing, optics, protocells, computing, or adaptive matter. Inspired by the transmission of signals among decentralized units in slime mold Physarum polycephalum, we introduce a combination of surfactants, self-assembly, and photochemistry to establish chemical signal transfer among droplets. To connect droplets that float at an air-water interface, surfactant triethylene glycol monododecylether (C12E3) is used for its ability to self-assemble into wires called myelins. We show how the trajectory of these myelins can be directed toward selected photoactive droplets upon UV exposure. To this end, we developed a strategy for photocontrolled Marangoni flow, which comprises (1) the liquid crystalline coating formed at the surface of an oleic acid/sodium oleate (OA/NaO) droplet when in contact with water, (2) a photoacid generator that protonates sodium oleate upon UV exposure and therefore disintegrates the coating, and (3) the surface tension gradient that is generated upon depletion of the surfactant from the air-water interface by the uncoated droplet. Therefore, localized UV exposure of selected OA/NaO droplets results in attraction of the myelins such that they establish reconfigurable connections that self-organize among the C12E3 and OA/NaO droplets. As an example of communication, we demonstrate how the myelins transfer fluorescent dyes, which are selectively delivered in the droplet interior upon photochemical regulation of the liquid crystalline coating.

Colloidal Self-Assembly: From Passive to Active Systems

Self-assembly fundamentally implies the organization of small sub-units into large structures or patterns without the intervention of specific local interactions. This process is commonly observed in nature, occurring at various scales ranging from atomic/molecular assembly to the formation of complex biological structures. Colloidal particles may serve as micrometer-scale surrogates for studying assembly, particularly for the poorly understood kinetic and dynamic processes at the atomic scale. Recent advances in colloidal self-assembly have enabled the programmable creation of novel materials with tailored properties. We here provide an overview and comparison of both passive and active colloidal self-assembly, with a discussion on the energy landscape and interactions governing both types. In the realm of passive colloidal assembly, many impressive and important structures have been realized, including colloidal molecules, one-dimensional chains, two-dimensional lattices, and three-dimensional crystals. In contrast, active colloidal self-assembly, driven by optical, electric, chemical, or other fields, involves more intricate dynamic processes, offering more flexibility and potential new applications. A comparative analysis underscores the critical distinctions between passive and active colloidal assemblies, highlighting the unique collective behaviors emerging in active systems. These behaviors encompass collective motion, motility-induced phase segregation, and exotic properties arising from out-of-equilibrium thermodynamics. Through this comparison, we aim to identify the future opportunities in active assembly research, which may suggest new application domains.

Modulating photothermocapillary interactions for logic operations at the air-water interface

We demonstrate a system for performing logical operations (OR, AND, and NOT gates) at the air-water interface based on Marangoni optical trapping and repulsion between photothermal particles. We identify a critical separation distance at which the trapped particle assemblies become unstable, providing insight into the potential for scaling to larger arrays of logic elements.

Emergent Collective Motion of Self-Propelled Condensate Droplets

Recently, there is much interest in droplet condensation on soft or liquid or liquidlike substrates. Droplets can deform soft and liquid interfaces resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g., increased nucleation, interdroplet attraction). Here, we describe a unique collective motion of condensate water droplets that emerges spontaneously when a solid substrate is covered with a thin oil film. Droplets move first in a serpentine, self-avoiding fashion before transitioning to circular motions. We show that this self-propulsion (with speeds in the 0.1-1  mm s^{-1} range) is fueled by the interfacial energy release upon merging with newly condensed but much smaller droplets. The resultant collective motion spans multiple length scales from submillimeter to several centimeters, with potentially important heat-transfer and water-harvesting applications.

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.

Irreversibility across a Nonreciprocal PT-Symmetry-Breaking Phase Transition

Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a nontrivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking.

Nonequilibrium structure formation in electrohydrodynamic emulsions

Application of an electric field across the interface of two fluids with low, but non-zero, conductivities gives rise to a sustained electrohydrodynamic (EHD) fluid flow. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force, a consequence of drops encountering disturbance electric fields around their neighbors. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal, an apparent violation of Newton's Third Law. The breadth of consequences due to these non-reciprocal interactions are vast: we show selected cases in two dimensions, where drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, where drops form stratified chains, or combine into a single dynamic sheet.

Brownian motors powered by nonreciprocal interactions

Traditional models for molecular (Brownian) motors predominantly depend on nonequilibrium driving, while particle interactions rigorously adhere to Newton's third law. However, numerous living and natural systems at various scales seem to defy this well-established law. In this study, we investigated the transport of mixed Brownian particles in a two-dimensional ratchet potential with nonreciprocal interactions. Our findings reveal that these nonreciprocal interactions can introduce a zero-mean nonequilibrium driving force. This force is capable of disrupting the thermodynamic equilibrium and inducing directed motion. The direction of this motion is determined by the asymmetry of the potential. Interestingly, the average velocity is a peaked function of the degree of nonreciprocity, while the effective diffusion consistently increases with the increase of nonreciprocity. There exists an optimal temperature or packing fraction at which the average velocity reaches its maximum value. We share a mechanism for particle rectification, devoid of particle-autonomous nonequilibrium drive, with potential usage in systems characterized by nonreciprocal interactions.

Photocharging of Carbon Nitride Thin Films for Controllable Manipulation of Droplet Force Gradient Sensors

Intentional generation, amplification, and discharging of chemical gradients is central to many nano- and micromanipulative technologies. We describe a straightforward strategy to direct chemical gradients inside a solution via local photoelectric surface charging of organic semiconducting thin films. We observed that the irradiation of carbon nitride thin films with ultraviolet light generates local and sustained surface charges in illuminated regions, inducing chemical gradients in adjacent solutions via charge-selective immobilization of surfactants onto the substrate. We studied these gradients using droplet force gradient sensors, complex emulsions with simultaneous and independent responsive modalities to transduce information on transient gradients in temperature, chemistry, and concentration via tilting, morphological reconfiguration, and chemotaxis. Fine control over the interaction between local, photoelectrically patterned, semiconducting carbon nitride thin films and their environment yields a new method to design chemomechanically responsive materials, potentially applicable to micromanipulative technologies including microfluidics, lab-on-a-chip devices, soft robotics, biochemical assays, and the sorting of colloids and cells.

Enhanced diffusion of tracer particles in nonreciprocal mixtures

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.

Spontaneous Demixing of Binary Colloidal Flocks

Population heterogeneity is ubiquitous among active living systems, but little is known about its role in determining their spatial organization and large-scale dynamics. Combining evidence from synthetic active fluids assembled from self-propelled colloidal particles along with theoretical predictions at the continuum scale, we demonstrate the spontaneous demixing of binary polar liquids within circular confinement. Our analysis reveals how both active speed heterogeneity and nonreciprocal repulsive interactions lead to self-sorting behavior. By establishing general principles for the self-organization of binary polar liquids, our findings highlight the specificity of multicomponent active systems.

Effect of speed fluctuations on the collective dynamics of active disks

Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate β. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of β, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.

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.

On-Demand Breaking of Action-Reaction Reciprocity between Magnetic Microdisks Using Global Stimuli

Coupled physical interactions induce emergent collective behaviors of many interacting objects. Nonreciprocity in the interactions generates unexpected behaviors. There is a lack of experimental model system that switches between the reciprocal and nonreciprocal regime on demand. Here, we study a system of magnetic microdisks that breaks action-reaction reciprocity via fluid-mediated hydrodynamic interactions, on demand. Via experiments and simulations, we demonstrate that nonreciprocal interactions generate self-propulsion-like behaviors of a pair of disks; group separation in collective of magnetically nonidentical disks; and decouples a part of the group from the rest. Our results could help in developing controllable microrobot collectives. Our approach highlights the effect of global stimuli in generating nonreciprocal interactions.

Photoactive and Intrinsically Fuel Sensing Metal-Organic Framework Motors for Tailoring Collective Behaviors of Active-Passive Colloids

Microorganisms display nonequilibrium predator-prey behaviors, such as chasing-escaping and schooling via chemotactic interactions. Even though artificial systems have revealed such biomimetic behaviors, switching between them by control over chemotactic interactions is rare. Here, a spindle-like iron-based metal-organic framework (MOF) colloidal motor which self-propels in glucose and H2 O2 , triggered by UV light is reported. These motors display intrinsic UV light-triggered fuel-dependent chemotactic interactions, which are used to tailor the collective dynamics of active-passive colloidal mixtures. In particular, the mixtures of active MOF motors with passive colloids exhibit distinctive "chasing-escaping" or "schooling" behaviors, depending on glucose or hydrogen peroxide being used as the fuel. The transition in the collective behaviors is attributed to an alteration in the sign of ionic diffusiophoretic interactions, resulting from a change in the ionic clouds produced. This study offers a new strategy on tuning the communication between active and passive colloids, which holds substantial potentials for fundamental research in active matter and practical applications in cargo delivery, chemical sensing, and particle segregation.

Droplet duos on water display pairing, autonomous motion, and periodic eruption

Under non-equilibrium conditions, liquid droplets dynamically couple with their milieu through the continuous flux of matter and energy, forming active systems capable of self-organizing functions reminiscent of those of living organisms. Among the various dynamic behaviors demonstrated by cells, the pairing of heterogeneous cell units is necessary to enable collective activity and cell fusion (to reprogram somatic cells). Furthermore, the cyclic occurrence of eruptive events such as necroptosis or explosive cell lysis is necessary to maintain cell functions. However, unlike the self-propulsion behavior of cells, cyclic cellular behavior involving pairing and eruption has not been successfully modeled using artificial systems. Here, we show that a simple droplet system based on quasi-immiscible hydrophobic oils (perfluorodecalin and decane) deposited on water, mimics such complex cellular dynamics. Perfluorodecalin and decane droplet duos form autonomously moving Janus or coaxial structures, depending on their volumes. Notably, the system with a coaxial structure demonstrates cyclic behavior, alternating between autonomous motion and eruption. Despite their complexity, the dynamic behaviors of the system are consistently explained in terms of the spreading properties of perfluorodecalin/decane duplex interfacial films.

Self-organization of primitive metabolic cycles due to non-reciprocal interactions

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how metabolic cycles, which power the non-equilibrium activity of cells, have come into existence in the first instances. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. Here, we propose an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can partner together in a cyclic reaction lead to their recruitment into self-organized functional structures. We uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features.

Ionic Liquid-in-Water Emulsions Stabilized by Molecular and Polymeric Surfactants

Ionic liquids have drawn notable attention for their unique solvent properties and use in applications such as batteries and chemical separations. While many ionic liquids are water-soluble, there are numerous examples of ionic liquids that are sufficiently hydrophobic to remain phase separated from water. However, relatively little is known about the stability and properties of ionic liquid-in-water emulsions. Here, we survey a series of ionic liquid-in-water emulsions stabilized by a range of ionic and nonionic molecular surfactants and polymers. To assess droplet stability and dynamics, we characterize the ionic liquid-surfactant interfacial tension, describe qualitative coarsening rates, and quantify droplet solubilization rate. In some instances, we observe unexpected spontaneous formation of complex double and triple emulsions. Our observations highlight approaches for ionic liquid emulsion formulation and provide insight into how to address challenges surrounding stabilization of ionic liquid-in-water droplets with molecular surfactants.

Responsive Janus droplets as modular sensory layers for the optical detection of bacteria

The field of biosensor development is fueled by innovations in new functional transduction materials and technologies. Material innovations promise to extend current sensor hardware limitations, reduce analysis costs, and ensure broad application of sensor methods. Optical sensors are particularly attractive because they enable sensitive and noninvasive analyte detection in near real-time. Optical transducers convert physical, chemical, or biological events into detectable changes in fluorescence, refractive index, or spectroscopic shifts. Thus, in addition to sophisticated biochemical selector designs, smart transducers can improve signal transmission and amplification, thereby greatly facilitating the practical applicability of biosensors, which, to date, is often hampered by complications such as difficult replication of reproducible selector-analyte interactions within a uniform and consistent sensing area. In this context, stimuli-responsive and optically active Janus emulsions, which are dispersions of kinetically stabilized biphasic fluid droplets, have emerged as a novel triggerable material platform that provides as a versatile and cost-effective alternative for the generation of reproducible, highly sensitive, and modular optical sensing layers. The intrinsic and unprecedented chemical-morphological-optical coupling inside Janus droplets has facilitated optical signal transduction and amplification in various chemo- and biosensor paradigms, which include examples for the rapid and cost-effective detection of major foodborne pathogens. These initial demonstrations resulted in detection limits that rival the capabilities of current commercial platforms. This trend article aims to present a conceptual summary of these initial efforts and to provide a concise and comprehensive overview of the pivotal kinetic and thermodynamic principles that govern the ability of Janus droplets to sensitively and selectively respond to and interact with bacteria.

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.

Darwin's agential materials: evolutionary implications of multiscale competency in developmental biology

A critical aspect of evolution is the layer of developmental physiology that operates between the genotype and the anatomical phenotype. While much work has addressed the evolution of developmental mechanisms and the evolvability of specific genetic architectures with emergent complexity, one aspect has not been sufficiently explored: the implications of morphogenetic problem-solving competencies for the evolutionary process itself. The cells that evolution works with are not passive components: rather, they have numerous capabilities for behavior because they derive from ancestral unicellular organisms with rich repertoires. In multicellular organisms, these capabilities must be tamed, and can be exploited, by the evolutionary process. Specifically, biological structures have a multiscale competency architecture where cells, tissues, and organs exhibit regulative plasticity-the ability to adjust to perturbations such as external injury or internal modifications and still accomplish specific adaptive tasks across metabolic, transcriptional, physiological, and anatomical problem spaces. Here, I review examples illustrating how physiological circuits guiding cellular collective behavior impart computational properties to the agential material that serves as substrate for the evolutionary process. I then explore the ways in which the collective intelligence of cells during morphogenesis affect evolution, providing a new perspective on the evolutionary search process. This key feature of the physiological software of life helps explain the remarkable speed and robustness of biological evolution, and sheds new light on the relationship between genomes and functional anatomical phenotypes.

Orbiting Self-Organization of Filament-Tethered Surface-Active Droplets

Dissipative chemical systems hold the potential to enable life-like behavior in synthetic matter, such as self-organization, motility, and dynamic switching between different states. Here, out-of-equilibrium self-organization is demonstrated by interconnected source and drain droplets at an air-water interface, which display dynamic behavior due to a hydrolysis reaction that generates a concentration gradient around the drain droplets. This concentration gradient interferes with the adhesion of self-assembled amphiphile filaments that grow from a source droplet. The chemical gradient sustains a unique orbiting of the drain droplet, which is proposed to be driven by the selective adhesion of the filaments to the front of the moving droplet, while filaments approaching from behind are destabilized upon contact with the hydrolysis product in the trail of the droplet. Potential applications are foreseen in the transfer of chemical signals amongst communicating droplets in rearranging networks, and the implementation of chemical reactions to drive complex positioning routines in life-like systems.

Toward droplets displaying life-like interaction behaviors

Developments in synthetic biology usually bring the conception of individual artificial cells. A key feature of living systems is, however, the interaction between individuals, in which living units can interact autonomously and display a role differentiation such as the case of entities chasing each other. On the other hand, droplets have become a very useful and exciting medium for modern microengineering and biomedical technologies. In this Perspective, we show a brief discussion-outlook of different approaches to recreate predator-prey interactions in both swimmer and crawling droplet systems toward a new generation of synthetic life with impact in both fundamental insights and relevant applications.

Gravitational settling of active droplets

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled-micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (α) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of α) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of α occurs for an active settling droplet is proposed.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Two-dimensional diffusiophoretic colloidal banding: optimizing the spatial and temporal design of solute sinks and sources

Diffusiophoresis refers to the phenomenon where colloidal particles move in response to solute concentration gradients. Existing studies on diffusiophoresis, both experimental and theoretical, primarily focus on the movement of colloidal particles in response to one-dimensional solute gradients. In this work, we numerically investigate the impact of two-dimensional solute gradients on the distribution of colloidal particles, i.e., colloidal banding, induced via diffusiophoresis. The solute gradients are generated by spatially arranged sources and sinks that emit/absorb a time-dependent solute molar rate. First we study a dipole system, i.e., one source and one sink, and discover that interdipole diffusion and molar rate decay timescales dictate colloidal banding. At timescales shorter than the interdipole diffusion timescale, we observe a rapid enhancement in particle enrichment around the source due to repulsion from the sink. However, at timescales longer than the interdipole diffusion timescale, the source and sink screen each other, leading to a slower enhancement. If the solute molar rate decays at the timescale of interdipole diffusion, an optimal separation distance is obtained such that particle enrichment is maximized. We find that the partition coefficient of solute at the interface between the source and bulk strongly impacts the optimal separation distance. Surprisingly, the diffusivity ratio of solute in the source and bulk has a much weaker impact on the optimal dipole separation distance. We also examine an octupole configuration, i.e., four sinks and four sources, arranged in a circle, and demonstrate that the geometric arrangement that maximizes enrichment depends on the radius of the circle. If the radius of the circle is small, it is preferred to have sources and sinks arranged in an alternating fashion. However, if the radius of the circle is large, a consecutive arrangement of sources and sinks is optimal. Our numerical framework introduces a novel method for spatially and temporally designing the banded structure of colloidal particles in two dimensions using diffusiophoresis and opens up new avenues in a field that has primarily focused on one-dimensional solute gradients.

Collective motion of active particles exhibiting non-reciprocal orientational interactions

We present a Brownian dynamics study of a 2D bath of active particles interacting among each other through usual steric interactions and, additionally, via non-reciprocal avoidant orientational interactions. We motivate them by the fact that the two flagella of the alga Chlamydomonas interact sterically with nearby surfaces such that a torque acts on the alga. As expected, in most cases such interactions disrupt the motility-induced particle clustering in active baths. Surprisingly, however, we find that the active particles can self-organize into collectively moving flocks if the range of non-reciprocal interactions is close to that of steric interactions. We observe that the flocking motion can manifest itself through a variety of structural forms, spanning from single dense bands to multiple moderately-dense stripes, which are highly dynamic. The flocking order parameter is found to be only weakly dependent on the underlying flock structure. Together with the variance of the local-density distribution, one can clearly group the flocking motion into the two separate band and dynamic-stripes states.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Self-Organization Emerging from Marangoni and Elastocapillary Effects Directed by Amphiphile Filament Connections

Self-organization of meso- and macroscale structures is a highly active research field that exploits a wide variety of physicochemical phenomena, including surface tension, Marangoni flow, and (elasto)capillary effects. The release of surface-active compounds generates Marangoni flows that cause repulsion, whereas capillary forces attract floating particles via the Cheerios effect. Typically, the interactions resulting from these effects are nonselective because the gradients involved are uniform. In this work, we unravel the mechanisms involved in the self-organization of amphiphile filaments that connect and attract droplets floating at the air-water interface, and we demonstrate their potential for directional gradient formation and thereby selective interaction. We simulate Marangoni flow patterns resulting from the release and depletion of amphiphile molecules by source and drain droplets, respectively, and we predict that these flow patterns direct the growth of filaments from the source droplets toward specific drain droplets, based on their amphiphile depletion rate. The interaction between such droplets is then investigated experimentally by charting the flow patterns in their surroundings, while the role of filaments in source-drain attraction is studied using microscopy. Based on these observations, we attribute attraction of drain droplets and even solid objects toward the source to elastocapillary effects. Finally, the insights from our simulations and experiments are combined to construct a droplet-based system in which the composition of drain droplets regulates their ability to attract filaments and as a consequence be attracted toward the source. Thereby, we provide a novel method through which directional attraction can be established in synthetic self-organizing systems and advance our understanding of how complexity arises from simple building blocks.

Phase-flip transition in volume-mismatched pairs of coupled 1-pentanol drops

We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop (≥ 3μL) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 μL in steps of 1μL, whereas the drop 2 volume was varied from 1 to 3 μL in steps of 0.5μL. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony-in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of >3.0μL between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was <2.0μL. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.

Dynamic ordering caused by a source-sink relation between two droplets

Two droplets composed of different chemicals, 1-decanol and liquid paraffin, floating on the water surface show characteristic co-responsive behavior. The presence of two different types of droplets in the system imposes an asymmetry that would not be possible with single droplets alone. The self-propulsion and interactions between droplets appear because surface active 1-decanol molecules provided by the source are absorbed by the paraffin sink thus generating an asymmetric surface tension gradient. This source-sink relation between droplets stabilizes and enhances the self-propulsion, and leads to a variety of dynamic structures including oscillations in the inter-droplet distance. We found that the character of time evolution also depends on the concentration of dye, Sudan Black B, initially used just to stain the decanol droplet. A simple mathematical model explains the transition between the stationary state and the oscillations as a Hopf bifurcation.

Chemically Tuning Attractive and Repulsive Interactions between Solubilizing Oil Droplets

Micellar solubilization is a transport process occurring in surfactant-stabilized emulsions that can lead to Marangoni flow and droplet motility. Active droplets exhibit self-propulsion and pairwise repulsion due to solubilization processes and/or solubilization products raising the droplet's interfacial tension. Here, we report emulsions with the opposite behavior, wherein solubilization decreases the interfacial tension and causes droplets to attract. We characterize the influence of oil chemical structure, nonionic surfactant structure, and surfactant concentration on the interfacial tensions and Marangoni flows of solubilizing oil-in-water drops. Three regimes corresponding to droplet "attraction", "repulsion" or "inactivity" are identified. We believe these studies contribute to a fundamental understanding of solubilization processes in emulsions and provide guidance as to how chemical parameters can influence the dynamics and chemotactic interactions between active droplets.