Chemically powered nanodimers

Positive Chemotactic Flasklike Colloidal Motors Propelled by Rotary FoF1-ATP Synthases

Living microorganisms can perform directed migration for foraging in response to a chemoattractant gradient. We report a biomimetic strategy that rotary FoF1-ATPase (adenosine triphosphatase)-propelled flasklike colloidal motors exhibit positive chemotaxis resembling the chemotactic behavior of bacteria. The streamlined flasklike colloidal particles are fabricated through polymerization, expansion, surface rupture, and re-polymerizing nanoemulsions composed of triblock copolymers and ribose. The as-synthesized particles enable the incorporation of thylakoid vesicles into the cavity, ensuring a geometric asymmetric nanoarchitecture. The chemical gradient in the neck channel across flasklike colloidal motors facilitates autonomous movement at a speed of 1.19 μm/s in a ΔpH value of 4. Computer simulations reveal the self-actuated flasklike colloidal motors driven by self-diffusiophoretic force. These flasklike colloidal motors display positive directional motion along an adenosine diphosphate (ADP) concentration gradient during adenosine triphosphate (ATP) synthesis. The positive chemotaxis is ascribed that the phosphorylation reaction occurring inside colloidal motors generates 2 distinct phoretic torques at the bottom and the opening owing to the diffusion of ADP, thereby a continuous reorientation motion. Such a biophysical strategy that nanosized rotary protein molecular motors propel the directional movement of a flasklike colloidal motor holds promise for designing new types of biomedical swimming nanobots.

Response of chemically active dimer motor in phase-separating binary fluid mixture: Motility regulation and self-aggregation

The design of synthetic chemically powered nanomotors often considers the fuel and product to be miscible. The propulsion properties of such motors can be altered if the binary fluid consisting of fuel and product is phase separating. The dynamical properties of a dimer motor in a phase-separating binary mixture are discussed. Depending on the strength of phase separation and the activity of the dimer, the single-motor propulsion velocity either decreases or reverses its direction. The velocity reversal is shown to be related to the generated fluid flow around the motor. The collective dynamics of the motors in such phase-separating fluid results in the formation of self-assembled structures.

Phoresis kernel theory for passive and active spheres with nonuniform phoretic mobility

By introducing geometry-based phoresis kernels, we establish a direct connection between the translational and rotational velocities of a phoretic sphere and the distributions of the driving fields or fluxes. The kernels quantify the local contribution of the field or flux to the particle dynamics. The field kernels for both passive and active particles share the same functional form, depending on the position-dependent surface phoretic mobility. For uniform phoretic mobility, the translational field kernel is proportional to the surface normal vector, while the rotational field kernel is zero; thus, a phoretic sphere with uniform phoretic mobility does not rotate. As case studies, we discuss examples of a self-phoretic axisymmetric particle influenced by a globally-driven field gradient, a general scenario for axisymmetric self-phoretic particle and two of its special cases, and a non-axisymmetric active particle.

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.

Clustering induces switching between phoretic and osmotic propulsion in active colloidal rafts

Active particles driven by chemical reactions are the subject of intense research to date due to their rich physics, being intrinsically far from equilibrium, and their multiple technological applications. Recent attention in this field is now shifting towards exploring the fascinating dynamics of active and passive mixtures. Here we realize active colloidal rafts, composed of a single catalytic particle encircled by several shells of passive microspheres, and assembled via light-activated chemophoresis. We show that the cluster propulsion mechanism transits from diffusiophoretic to diffusioosmotic as the number of colloidal shells increases. Using the Lorentz reciprocal theorem, we demonstrate that in large clusters self-propulsion emerges by considering the hydrodynamic flow via the diffusioosmotic response of the substrate. The dynamics in our active colloidal rafts are governed by the interplay between phoretic and osmotic effects. Thus, our work highlights their importance in understanding the rich physics of active catalytic systems.

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.

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.

Minimal numerical ingredients describe chemical microswimmers' 3-D motion

The underlying mechanisms and physics of catalytic Janus microswimmers is highly complex, requiring details of the associated phoretic fields and the physiochemical properties of catalyst, particle, boundaries, and the fuel used. Therefore, developing a minimal (and more general) model capable of capturing the overall dynamics of these autonomous particles is highly desirable. In the presented work, we demonstrate that a coarse-grained dissipative particle-hydrodynamics model is capable of describing the behaviour of various chemical microswimmer systems. Specifically, we show how a competing balance between hydrodynamic interactions experienced by a squirmer in the presence of a substrate, gravity, and mass and shape asymmetries can reproduce a range of dynamics seen in different experimental systems. We hope that our general model will inspire further synthetic work where various modes of swimmer motion can be encoded via shape and mass during fabrication, helping to realise the still outstanding goal of microswimmers capable of complex 3-D behaviour.

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

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

Active self-assembly of colloidal machines with passive rotational parts via coordination of phoresis and osmosis

The organization of microscopic objects into specific structures with movable parts is a prerequisite for building sophisticated micromachines with complex functions, as exemplified by their macroscopic counterparts. Here we report the self-assembly of active and passive colloids into micromachinery with passive rotational parts. Depending on the attachment of the active colloid to a substrate, which varies the degrees of free freedom of the assembly, colloidal machines with rich internal rotational dynamics are realized. Energetic analysis reveals that the energy efficiency increases with the degrees of freedom of the machine. The experimental results can be rationalized by the cooperation of phoretic interaction and osmotic flow encoded in the shape of the active colloid, which site-specifically binds and exerts a torque to passive colloids, supported by finite element calculations and mesoscale simulations. Our work offers a new design principle that utilizes nonequilibrium interfacial phenomena for spontaneous construction of multiple-component reconfigurable micromachinery.

Isotropic active colloids: explicit vs. implicit descriptions of propulsion mechanisms

Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of activity. Here, we take advantage of a recent two-dimensional model of isotropic active particles whose propulsion originates from the interactions between solute particles in the bath. The colloid catalyzes a chemical reaction in its vicinity, which results in a local phase separation of solute particles, and the density fluctuations of solute particles cause the enhanced diffusion of the colloid. In this paper, we investigate an assembly of such active particles, using (i) an explicit model, where the microscopic dynamics of the solute particles is accounted for; and (ii) an implicit model, whose parameters are inferred from the explicit model at infinite dilution. In the explicit solute model, the long-time diffusion coefficient of the active colloids strongly decreases with density, an effect which is not captured by the derived implicit model. This suggests that classical models, which usually decouple pair interactions from activity, fail to describe collective dynamics in active colloidal systems driven by solute-solute interactions.

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.

Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation

We study a two-dimensional model of an active isotropic colloid whose propulsion is linked to the interactions between solute particles of the bath. The colloid catalyzes a chemical reaction in its vicinity, that yields a local phase separation of solute particles. The density fluctuations of solute particles result in the enhanced diffusion of the colloid. Using numerical simulations, we thoroughly investigate the conditions under which activity occurs, and we establish a state diagram for the activity of the colloid as a function of the parameters of the model. We use the generated data to unravel a key observable that controls the existence and the intensity of activity: The filling fraction of the reaction area. Remarkably, we finally show that propulsion also occurs in three-dimensional geometries, which confirms the interest of this mechanism for experimental applications.

Clustering of self-thermophilic asymmetric dimers: the relevance of hydrodynamics

Self-thermophilic dimers are characterized by a net phoretic attraction which, in combination with hydrodynamic interactions, results in the formation of crystalline-like aggregates. To distinguish the effect of the different contributions is frequently an important challenge. We present a simulation investigation done in parallel in the presence and the absence of hydrodynamic interactions for the case of asymmetric self-thermophoretic dimers. In the absence of hydrodynamics, the clusters have the standard heads-in configurations. In contrast, in the presence of hydrodynamics, clusters with heads-in conformation are being formed, in which dimers with their propulsion velocity pointing out of the cluster are assembled and stabilized by strong hydrodynamic osmotic flows. Significant variation in the material properties is to be expected from such differences in the collective behavior, whose understanding and control is of great relevance for the development of new synthetic active materials.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics

Most computer simulations of molecular dynamics take place under equilibrium conditions-in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.

Self-phoretic Brownian dynamics simulations

A realistic and effective model to simulate phoretic Brownian dynamics swimmers based on the general form of the thermophoretic force is here presented. The collective behavior of self-phoretic dimers is investigated with this model and compared with two simpler versions, allowing the understanding of the subtle interplay of steric interactions, propulsion, and phoretic effects. The phoretic Brownian dynamics method has control parameters which can be tuned to closely map the properties of experiments or simulations with explicit solvent, in particular those performed with multiparticle collision dynamics. The combination of the phoretic Brownian method and multiparticle collision dynamics is a powerful tool to precisely identify the importance of hydrodynamic interactions in systems of self-phoretic swimmers.

The dynamics of chemically propelled dimer motor on a pinning substrate

The dynamics of self-propelled micro-motors, in a thin fluid film containing an attractive substrate, is investigated by means of a particle-based simulation. A chemically powered sphere dimer, consisting of a...

Spontaneous propulsion of an isotropic colloid in a phase-separating environment

The motion of active colloids is generally achieved through their anisotropy, as exemplified by Janus colloids. Recently, there was a growing interest in the propulsion of isotropic colloids, which requires some local symmetry breaking. Although several mechanisms for such propulsion were proposed, little is known about the role played by the interactions within the environment of the colloid, which can have a dramatic effect on its propulsion. Here, we propose a minimal model of an isotropic colloid in a bath of solute particles that interact with each other. These interactions lead to a spontaneous phase transition close to the colloid, to directed motion of the colloid over very long timescales and to significantly enhanced diffusion, in spite of the crowding induced by solute particles. We determine the range of parameters where this effect is observable in the model, and we propose an effective Langevin equation that accounts for it and allows one to determine the different contributions at stake in self-propulsion and enhanced diffusion.

Real-time temperature measurement in stochastic rotation dynamics

Many physical and chemical processes involve energy change with rates that depend sensitively on local temperature. Important examples include heterogeneously catalyzed reactions and activated desorption. Because of the multiscale nature of such systems, it is desirable to connect the macroscopic world of continuous hydrodynamic and temperature fields to mesoscopic particle-based simulations with discrete particle events. In this work we show how to achieve real-time measurement of the local temperature in stochastic rotation dynamics (SRD), a mesoscale method particularly well suited for problems involving hydrodynamic flows with thermal fluctuations. We employ ensemble averaging to achieve local temperature measurement in dynamically changing environments. After validation by heat diffusion between two isothermal plates, heating of walls by a hot strip, and by temperature programed desorption, we apply the method to a case of a model flow reactor with temperature-sensitive heterogeneously catalyzed reactions on solid spherical catalysts. In this model, adsorption, chemical reactions, and desorption are explicitly tracked on the catalyst surface. This work opens the door for future projects where SRD is used to couple hydrodynamic flows and thermal fluctuations to solids with complex temperature-dependent surface mechanisms.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Active spheres induce Marangoni flows that drive collective dynamics

For monolayers of chemically active particles at a fluid interface, collective dynamics is predicted to arise owing to activity-induced Marangoni flow even if the particles are not self-propelled. Here, we test this prediction by employing a monolayer of spherically symmetric active [Formula: see text] particles located at an oil-water interface with or without addition of a nonionic surfactant. Due to the spherical symmetry, an individual particle does not self-propel. However, the gradients produced by the photochemical fuel degradation give rise to long-ranged Marangoni flows. For the case in which surfactant is added to the system, we indeed observe the emergence of collective motion, with dynamics dependent on the particle coverage of the monolayer. The experimental observations are discussed within the framework of a simple theoretical mean-field model.

The dynamics and self-assembly of chemically self-propelled sphere dimers

The dynamics of chemically powered sphere dimers at the micro- and nano-scales confined in a quasi-two-dimensional geometry are investigated. The dimer consists of a Janus particle and a non-catalytic sphere. A chemical reaction taking place on the catalytic surface of the Janus particle creates asymmetric concentration gradients that give rise to the self-propulsion of both rotation and translation of the dimer. Due to the chemical interactions, ensembles of dimers spontaneously form anti-parallel aligned doublets that exhibit the same rotation direction and lose translational motion. The chirality of the dimer plays an important role in the process of doublet formation. The study displays new collective dynamics and structures when both translational and rotational self-propulsion occur.

Multi-particle collision dynamics with a non-ideal equation of state. I

The method of multi-particle collision dynamics (MPCD) and its different implementations are commonly used in the field of soft matter physics to simulate fluid flow at the micron scale. Typically, the coarse-grained fluid particles are described by the equation of state of an ideal gas, and the fluid is rather compressible. This is in contrast to conventional fluids, which are incompressible for velocities much below the speed of sound, and can cause inhomogeneities in density. We propose an algorithm for MPCD with a modified collision rule that results in a non-ideal equation of state and a significantly decreased compressibility. It allows simulations at less computational costs compared to conventional MPCD algorithms. We derive analytic expressions for the equation of state and the corresponding compressibility as well as shear viscosity. They show overall very good agreement with simulations, where we determine the pressure by simulating a quiet bulk fluid and the shear viscosity by simulating a linear shear flow and a Poiseuille flow.

Self-Motility of an Active Particle Induced by Correlations in the Surrounding Solution

Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a nonvanishing correlation length of the surrounding solution. This mechanism can drive self-motility of a chemically active particle. Numerical estimates indicate that the velocity can reach micrometers per second. The predicted phenomenology includes a bilinear dependence of the velocity on the activity and a possible double velocity reversal upon varying the correlation length.

Unravelling the role of phoretic and hydrodynamic interactions in active colloidal suspensions

Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external force. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically the suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamically resolved solute-mediated phoretic interactions and solvent-mediated hydrodynamic interactions. Our results show that the system displays different scenarios at changing the colloid-solute affinity and it develops a cluster phase in the chemoattractive case. We study the statistics of cluster sizes and cluster morphologies for different magnitudes of colloidal activity. Finally, we provide evidences that hydrodynamics plays a relevant role in the aggregation kinetics and cluster morphology, significantly hindering cluster growth.

Self-propelled torus colloids

Suspensions of chemically powered self-propelled colloidal particles are examples of active matter systems with interesting properties. While simple spherical Janus particles are often studied, it is known that geometry is important and recent experiments have shown that chemically active torus-shaped colloids behave differently from spherical colloids. In this paper, coarse-grained microscopic simulations of the dynamics of self-diffusiophoretic torus colloids are carried out in bulk solution in order to study how torus geometric factors influence their active motion. The concentration and velocity fields are key ingredients in self-diffusiophoretic propulsion, and the forms that these fields take in the colloid vicinity are shown to be strong functions of torus geometric parameters such as the torus hole size and thickness of the torus tube. This work utilizes a method where self-diffusiophoretic torus colloids with various geometric and dynamical characteristics can be built and studied in fluid media that include chemical reactions and fluid flows. The model can be used to investigate the collective properties of these colloids and their dynamics in confined systems, topics that are of general importance for applications that use colloidal motors with complex geometries.

Current inversion in a periodically driven two-dimensional Brownian ratchet

It is well known that Brownian ratchets can exhibit current reversals, wherein the sign of the current switches as a function of the driving frequency. We introduce a spatial discretization of such a two-dimensional Brownian ratchet to enable spectral methods that efficiently compute those currents. These discrete-space models provide a convenient way to study the Markovian dynamics conditioned upon generating particular values of the currents. By studying such conditioned processes, we demonstrate that low-frequency negative values of current arise from typical events and high-frequency positive values of current arises from rare events. We demonstrate how these observations can inform the sculpting of time-dependent potential landscapes with a specific frequency response.

Chemically Active Particles: From One to Few on the Way to Many

Chemically active particles suspended in a liquid solution can achieve self-motility by locally changing the chemical composition of the solution via catalytic reactions at their surfaces. They operate intrinsically out of equilibrium, continuously extracting free energy from the environment to power the dissipative self-motility. The effective interactions involving active particles are, in general, nonreciprocal and anisotropic, even if the particles have simple shapes (e.g., Janus spheres). Accordingly, for chemically active particles a very rich behavior of collective motion and self-assembly may be expected to emerge, including phenomena such as microphase separation in the form of kinetically stable, finite-sized aggregates. Here, I succinctly review a number of recent experimental studies that demonstrate the self-assembly of structures, involving chemically active Janus particles, which exhibit various patterns of motion. These examples illustrate concepts such as "motors made out of motors" (as suggestively named by Fischer [Fischer, P. Nat. Phys. 2018, 14, 1072]). The dynamics of assembly and structure formation observed in these systems can provide benchmark, in-depth testing of the current understanding of motion and effective interactions produced by chemical activity. Finally, one notes that these significant achievements are likely just the beginning of the field. Recently reported particles endowed with time-dependent chemical activity or switchable reaction mechanisms open the way for exciting developments, such as periodic reshaping of self-assembled structures based on man-made internal clocks.

Separation of nanoparticles via surfing on chemical wavefronts

The separation of micro and nanoscale colloids is a necessary step in most biological microassay techniques, and is a common practice in microchemical processing. Chemical waves are frequently encountered in biochemical systems driven far from equilibrium. Here, we put forward a strategy for separating small suspending colloids by means of their surfing on substrate chemical wavefronts. The colloids with catalytic activities sensitive to the substrates are activated to show self-propulsion and consequently exhibit a chemotactic response to the traveling wavefronts, which results in their spontaneous separation from the multicomponent complex mixture via self-diffusiophoresis. The dynamics of the process is analyzed through a particle-based simulation. In addition, it is found that separation can be carried out according to particle size. The mechanisms underpinning the chemical and physical separation processes are discussed, and the dependencies on the reaction rate constant and particle size are presented. The results may prove relevant for further experimental and theoretical studies of separation in complex active environments.

Studying polymer diffusiophoresis with non-equilibrium molecular dynamics

We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute that has a concentration gradient and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition, we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows.

Surface Wettability-Directed Propulsion of Glucose-Powered Nanoflask Motors

Chemically driven colloidal motors capable of implementing different movements under a common environment are of great importance for various complex tasks. However, the key parameters underlying different motion behaviors are incompletely understood. Here, we demonstrate that carbonaceous nanoflask (CNF) motors move spontaneously in glucose powered by the cascade reaction of glucose oxidase and catalase, and their directional propulsion can be premeditated by controlling the surface wettability of nanomotors. The hydrophilic CNF motors move from the round-bottom to the opening neck (backward), whereas the hydrophobic CNF motors swim from the opening neck to the round-bottom (forward). We demonstrate that the backward motion of the hydrophilic CNF motors is driven by the local glucose gradient due to self-diffusiophoresis, and the forward movement of the hydrophobic CNF motors is caused by the locally produced glucose acid gradient. The fluid simulation reveals that the hydrophilic and hydrophobic CNF motors correspond to the puller and pusher models, respectively. Our study offers a minimal strategy to manipulate the direction of motion of motors for specific applications and to change the hydrodynamic behaviors of glucose-powered motors.

Mesoscopic simulations of anisotropic chemically powered nanomotors

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Nonequilibrium atomistic molecular dynamics simulation of tubular nanomotor propelled by bubble propulsion

We develop a molecular nanoscaled model for tubular motors propelled by bubble propulsion. The motor is modeled by a carbon nanotube, and the bubble is represented by a particle interacting with water by a time-dependent potential. Effects of liquid viscosity, fuel concentration, geometry, and size of the tube on the performance of the motor are effectively encoded into two parameters: time scales of the bubble expansion and bubble formation. Our results are qualitatively consistent with experimental data of much larger motors. Simulations suggest that (i) the displacement of the tube is optimized if two time scales are as short as possible, (ii) the compromise between the performance and fuel consumption is achieved if the bubble formation time is shorter than the velocity correlation time of the tube, (iii) the motor efficiency is higher with slow expansion, short formation of the bubble than fast growth but long formation time, and (iv) the tube is propelled by strong forces on the order of mN, reaching high speeds up to ∼60 m/s. Our simulation may be useful for refining and encouraging future experimental work on nanomotors having the size of a few nanometers. The tiny size and high speed motors could have great potential applications in real life.

Enhanced Diffusion of Catalytically Active Enzymes

The past decade has seen an increasing number of investigations into enhanced diffusion of catalytically active enzymes. These studies suggested that enzymes are actively propelled as they catalyze reactions or bind with ligands (e.g., substrates or inhibitors). In this Outlook, we chronologically summarize and discuss the experimental observations and theoretical interpretations and emphasize the potential contradictions in these efforts. We point out that the existing multimeric forms of enzymes or isozymes may cause artifacts in measurements and that the conformational changes upon substrate binding are usually not sufficient to give rise to a diffusion enhancement greater than 30%. Therefore, more rigorous experiments and a more comprehensive theory are urgently needed to quantitatively validate and describe the enhanced enzyme diffusion.

A hybrid method for micro-mesoscopic stochastic simulation of reaction-diffusion systems

The present paper introduces a new micro-meso hybrid algorithm based on the Ghost Cell Method concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modeled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm. No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving mass, energy and momentum in the collision and free streaming steps. The new algorithm is tested on three reaction-diffusion systems. In all the systems studied, very good agreement with the deterministic solutions of the corresponding differential equations is obtained. In addition, it has been shown that proper discretization of the computational domain results in significant speed-ups in comparison with the full RMPC algorithm.

Effective Interactions between Chemically Active Colloids and Interfaces

Chemically active colloids can achieve force- and torque-free motility ("self-propulsion") via the promotion, on their surface, of catalytic chemical reactions involving the surrounding solution. Such systems are valuable both from a theoretical perspective, serving as paradigms for nonequilibrium processes, as well as from an application viewpoint, according to which active colloids are envisioned to play the role of carriers ("engines") in novel lab-on-a-chip devices. The motion of such colloids is intrinsically connected with a "chemical field", i.e., the distribution near the colloid of the number densities of the various chemical species present in the solution, and with the hydrodynamic flow of the solution around the particle. In most of the envisioned applications, and in virtually all reported experimental studies, the active colloids operate under spatial confinement (e.g., within a microfluidic channel, a drop, a free-standing liquid film, etc.). In such cases, the chemical field and the hydrodynamic flow associated with an active colloid are influenced by any nearby confining surfaces, and these disturbances couple back to the particle. Thus, an effective interaction with the spatial confinement arises. Consequently, the particle is endowed with means to perceive and to respond to its environment. Understanding these effective interactions, finding the key parameters which control them, and designing particles with desired, preconfigured responses to given environments, require interdisciplinary approaches which synergistically integrate methods and knowledge from physics, chemistry, engineering, and materials science. Here we review how, via simple models of chemical activity and self-phoretic motion, progress has recently been made in understanding the basic physical principles behind the complex behaviors exhibited by active particles near interfaces. First, we consider the occurrence of "interface-bounded" steady states of chemically active colloids near simple, nonresponsive interfaces. Examples include particles "sliding" along, or "hovering" above, a hard planar wall while inducing hydrodynamic flow of the solution. These states lay the foundations for concepts like the guidance of particles by the topography of the wall. We continue to discuss responsive interfaces: a suitable chemical patterning of a planar wall allows one to bring the particles into states of motion which are spatially localized (e.g., within chemical stripes or along chemical steps). These occur due to the wall responding to the activity-induced chemical gradients by generating osmotic flows, which encode the surface-chemistry of the wall. Finally, we discuss how, via activity-induced Marangoni stresses, long-ranged effective interactions emerge from the strong hydrodynamic response of fluid interfaces. These examples highlight how in this context a desired behavior can be potentially selected by tuning suitable parameters (e.g., the phoretic mobility of the particle, or the strength of the Marangoni stress at an interface). This can be accomplished via a judicious design of the surface chemistry of the particle and of the boundary, or by the choice of the chemical reaction in solution.

Effective squirmer models for self-phoretic chemically active spherical colloids

Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic-slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) --as employed in many experimental studies-- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers (S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)). Accordingly, intuitively appealing analogies of "pusher/puller/neutral" squirmers arise naturally. Within the framework of self-diffusiophoresis we illustrate the above-mentioned mapping and the corresponding flows in an unbounded fluid for a number of choices of the activity function (i.e., the spatial distribution and the type of chemical reactions across the surface of the particle). We use the central collision of two active particles as a simple, paradigmatic case for demonstrating that in the presence of other particles or boundaries the behavior of chemically active colloids may be qualitatively different, even in the far field, from the one exhibited by the corresponding "effective squirmer", obtained from the mapping in an unbounded fluid. This emphasizes that understanding the collective behavior and the dynamics under geometrical confinement of chemically active particles necessarily requires to explicitly account for the dependence of the hydrodynamic interactions on the distribution of chemical species resulting from the activity of the particles.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Micro-/Nanorobots Propelled by Oscillating Magnetic Fields

Recent strides in micro- and nanomanufacturing technologies have sparked the development of micro-/nanorobots with enhanced power and functionality. Due to the advantages of on-demand motion control, long lifetime, and great biocompatibility, magnetic propelled micro-/nanorobots have exhibited considerable promise in the fields of drug delivery, biosensing, bioimaging, and environmental remediation. The magnetic fields which provide energy for propulsion can be categorized into rotating and oscillating magnetic fields. In this review, recent developments in oscillating magnetic propelled micro-/nanorobot fabrication techniques (such as electrodeposition, self-assembly, electron beam evaporation, and three-dimensional (3D) direct laser writing) are summarized. The motion mechanism of oscillating magnetic propelled micro-/nanorobots are also discussed, including wagging propulsion, surface walker propulsion, and scallop propulsion. With continuous innovation, micro-/nanorobots can become a promising candidate for future applications in the biomedical field. As a step toward designing and building such micro-/nanorobots, several types of common fabrication techniques are briefly introduced. Then, we focus on three propulsion mechanisms of micro-/nanorobots in oscillation magnetic fields: (1) wagging propulsion; (2) surface walker; and (3) scallop propulsion. Finally, a summary table is provided to compare the abilities of different micro-/nanorobots driven by oscillating magnetic fields.