Self-assembly of chemical shakers.

Chemical shakers are active particles with zero propulsion velocity whose activity derives from chemical reactions on portions of their surfaces. Although they do not move, except through Brownian motion, the nonequilibrium concentration and velocity fields that they generate endow them with properties that differ from their equilibrium counterparts. In particular, collections of such shakers can actively move, reorient, and self-assemble into various cluster states, which are the subject of this paper. Elongated chemical shakers constructed from linked catalytic and noncatalytic spheres are considered, and it is shown how hydrodynamic, chemotactic, and shape-dependent interactions give rise to various self-assembled shaker structures. The chemical forces responsible for cluster formation are described in terms of a model based on pair-wise additive contributions. The forms of the self-assembled structures can be varied by changing the chemostat concentrations that control the nonequilibrium state. The resulting structures and their manipulation through chemical means suggest ways to construct a class of active materials for applications.

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.

Chemical Logic Gates on Active Colloids.

Recent studies have shown that active colloidal motors using enzymatic reactions for propulsion hold special promise for applications in fields ranging from biology to material science. It will be desirable to have active colloids with capability of computation so that they can act autonomously to sense their surroundings and alter their own dynamics. It is shown how small chemical networks that make use of enzymatic chemical reactions on the colloid surface can be used to construct motor-based chemical logic gates. The basic features of coupled enzymatic reactions that are responsible for propulsion and underlie the construction and function of chemical gates are described using continuum theory and molecular simulation. Examples are given that show how colloids with specific chemical logic gates, can perform simple sensing tasks. Due to the diverse functions of different enzyme gates, operating alone or in circuits, the work presented here supports the suggestion that synthetic motors using such gates could be designed to operate in an autonomous way in order to complete complicated tasks.

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

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

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.

Multifunctional Chiral Chemically-Powered Micropropellers for Cargo Transport and Manipulation.

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

Inertial effects on rectification and diffusion of active Brownian particles in an asymmetric channel.

Micro- and nano-swimmers, moving in a fluid solvent confined by structures that produce entropic barriers, are often described by overdamped active Brownian particle dynamics, where viscous effects are large and inertia plays no role. However, inertial effects should be considered for confined swimmers moving in media where viscous effects are no longer dominant. Here, we study how inertia affects the rectification and diffusion of self-propelled particles in a two-dimensional, asymmetric channel. We show that most of the particles accumulate at the channel walls as the masses of the particles increase. Furthermore, the average particle velocity has a maximum as a function of the mass, indicating that particles with an optimal mass Mop * can be sorted from a mixture with particles of other masses. In particular, we find that the effective diffusion coefficient exhibits an enhanced diffusion peak as a function of the mass, which is a signature of the accumulation of most of the particles at the channel walls. The dependence of Mop * on the rotational diffusion rate, self-propulsion force, aspect ratio of the channel, and active torque is also determined. The results of this study could stimulate the development of strategies for controlling the diffusion of self-propelled particles in entropic ratchet systems.

Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids.

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

Self-propelled 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.

Active Matter, Microreversibility, and Thermodynamics.

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

The 2020 motile active matter roadmap.

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

Active rotational dynamics of a self-diffusiophoretic colloidal motor.

The dynamics of a spherical chemically-powered synthetic colloidal motor that operates by a self-diffusiophoretic mechanism and has a catalytic domain of arbitrary shape is studied using both continuum theory and particle-based simulations. The motor executes active rotational motion when self-generated concentration gradients and interactions between the chemical species and colloidal motor surface break spherical symmetry. Local variations of chemical reaction rates on the motor catalytic surface with catalytic domain sizes and shapes provide such broken symmetry conditions. A continuum theoretical description of the active rotational motion is given, along with the results of particle-based simulations of the active dynamics. From these results a detailed description of the factors responsible for the active rotational dynamics can be given. Since active rotational motion often plays a significant part in the nature of the collective dynamics of many-motor systems and can be used to control motor motion in targeted cargo transport, our results should find applications beyond those considered here.

From single particle motion to collective dynamics in Janus motor systems.

The single-particle and collective dynamics of systems comprising Janus motors, solvent, and reactive solute species maintained in nonequilibrium states are investigated. Reversible catalytic reactions with the solute species take place on the catalytic faces of the motors, and the nonequilibrium states are established either by imposing constant-concentration reservoirs that feed and remove reactive species or through out-of-equilibrium fluid phase reactions. We consider general intermolecular interactions between the Janus motor hemispheres and the reactive species. For single motors, we show that the reaction rate depends nonlinearly on an applied external force when the system is displaced far from equilibrium. We also show that a finite-time fluctuation formula derived for fixed catalytic particles describes the nonequilibrium reactive fluctuations of moving Janus motors. Simulation of the collective dynamics of small ensembles of Janus motors with reversible kinetics under nonequilibrium conditions is carried out, and the spatial and orientational correlations of dynamic cluster states are discussed. The conditions leading to the instability of the homogeneous motor distribution and the onset of nonequilibrium dynamical clustering are described.

Nonequilibrium thermodynamics and boundary conditions for reaction and transport in heterogeneous media.

Nonequilibrium interfacial thermodynamics is formulated in the presence of surface reactions for the study of diffusiophoresis in isothermal systems. As a consequence of microreversibility and Onsager-Casimir reciprocal relations, diffusiophoresis, i.e., the coupling of the tangential components of the pressure tensor to the concentration gradients of solute species, has a reciprocal effect where the interfacial currents of solutes are coupled to the slip velocity. The presence of surface reactions is shown to modify the diffusiophoretic and reciprocal effects at the fluid-solid interface. The thin-layer approximation is used to describe the solution flowing near a reactive solid interface. Analytic formulas describing the diffusiophoretic and reciprocal effects are deduced in the thin-layer approximation and tested numerically for the Poiseuille flow of a solution between catalytic planar surfaces.

Synthetic Nanomotors: Working Together through Chemistry.

Active matter, some of whose constituent elements are active agents that can move autonomously, behaves very differently from matter without such agents. The active agents can self-assemble into structures with a variety of forms and dynamical properties. Swarming, where groups of living agents move cooperatively, is commonly observed in the biological realm, but it is also seen in the physical realm in systems containing small synthetic motors. The existence of diverse forms of self-assembled structures has stimulated the search for new applications that involve active matter. We consider active systems where the agents are synthetic chemically powered motors with various shapes and sizes that operate by phoretic mechanisms, especially self-diffusiophoresis. These motors are able to move autonomously in solution by consuming fuel from their environment. Chemical reactions take place on catalytic portions of the motor surface and give rise to concentration gradients that lead to directed motion. They can operate in this way only if the chemical composition of the system is maintained in a nonequilibrium state since no net fluxes are possible in a system at equilibrium. In contrast to many other active systems, chemistry plays an essential part in determining the properties of the collective dynamics and self-assembly of these chemically powered motor systems. The inhomogeneous concentration fields that result from asymmetric motor reactions are felt by other motors in the system and strongly influence how they move. This chemical coupling effect often dominates other interactions due to fluid flow fields and direct interactions among motors and determines the form that the collective dynamics takes. Since we consider small motors with micrometer and nanometer sizes, thermal fluctuations are strong and cannot be neglected. The media in which the motors operate may not be simple and may contain crowding agents or molecular filaments that influence how the motors assemble and move. The collective motion is also influenced by the chemical gradients that arise from reactions in the surrounding medium. By adopting a microscopic perspective, where the motors, fluid environment, and crowding elements are treated at the coarse-grained molecular level, all of the many-body interactions that give rise to the collective behavior naturally emerge from the molecular dynamics. Through simulations and theory, this Account describes how active matter made from chemically powered nanomotors moving in simple and more complicated media can form different dynamical structures that are strongly influenced by interactions arising from cooperative chemical reactions on the motor surfaces.

Chemically Propelled Motors Navigate Chemical Patterns.

Very small synthetic motors that use chemical reactions to drive their motion are being studied widely because of their potential applications, which often involve active transport and dynamics on nanoscales. Like biological molecular machines, they must be able to perform their tasks in complex, highly fluctuating environments that can form chemical patterns with diverse structures. Motors in such systems can actively assemble into dynamic clusters and other unique nonequilibrium states. It is shown how chemical patterns with small characteristic dimensions may be utilized to suppress rotational Brownian motions of motors and guide them to move along prescribed paths, properties that can be exploited in applications. In systems with larger pattern length scales, domains can serve as catch basins for motors through chemotactic effects. The resulting collective motor dynamics in such confining domains can be used to explore new aspects of active particle collective dynamics or promote specific types of active self-assembly. More generally, when chemically self-propelled motors operate in far-from-equilibrium active chemical media the variety of possible phenomena and the scope of their potential applications are substantially increased.

Diffusiophoretically induced interactions between chemically active and inert particles.

In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and a moving inert sphere, and second, freely moving reactive and inert spheres. The continuum reaction-diffusion and Stokes equations are solved analytically for these systems and microscopic simulations of the dynamics are carried out. Although the relative velocities of the spheres are very similar in the two systems, the local and global structures of streamlines and the flow velocity fields are found to be quite different. For freely moving spheres, when the two spheres approach each other the flow generated by the inert sphere through diffusiophoresis drags the reactive sphere towards it. This leads to a self-assembled dimer motor that is able to propel itself in solution. The fluid flow field at the moment of dimer formation changes direction. The ratio of sphere sizes in the dimer influences the characteristics of the flow fields, and this feature suggests that active self-assembly of spherical colloidal particles may be manipulated by sphere-size changes in such reactive systems.

Dynamics of Janus motors with microscopically reversible kinetics.

Janus motors with chemically active and inactive hemispheres can operate only under nonequilibrium conditions where detailed balance is broken by fluxes of chemical species that establish a nonequilibrium state. A microscopic model for reversible reactive collisions on a Janus motor surface is constructed and shown to satisfy detailed balance. The model is used to study Janus particle reactive dynamics in systems at equilibrium where generalized chemical rate laws that include time-dependent rate coefficients with power-law behavior are shown to describe reaction rates. While maintaining reversible reactions on the Janus catalytic hemisphere, the system is then driven into a nonequilibrium steady state by fluxes of chemical species that control the chemical affinity. The statistical properties of the self-propelled Janus motor in this nonequilibrium steady state are investigated and compared with the predictions of a fluctuating thermodynamics theory. The model has utility beyond the examples presented here, since it allows one to explore various aspects of nonequilibrium fluctuations in systems with self-diffusiophoretic motors from a microscopic perspective.

Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles.

The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions at the interface between the fluid and the particle. These equations are consistent with microreversibility and the Onsager-Casimir reciprocal relations between affinities and currents and provide a thermodynamically consistent basis for the investigation of the dynamics of active particles propelled by diffusiophoretic mechanisms.