Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis

An Account on BiVO4 as Photocatalytic Active Matter

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

Swarm Autonomy: From Agent Functionalization to Machine Intelligence

Swarm behaviors are common in nature, where individual organisms collaborate via perception, communication, and adaptation. Emulating these dynamics, large groups of active agents can self-organize through localized interactions, giving rise to complex swarm behaviors, which exhibit potential for applications across various domains. This review presents a comprehensive summary and perspective of synthetic swarms, to bridge the gap between the microscale individual agents and potential applications of synthetic swarms. It is begun by examining active agents, the fundamental units of synthetic swarms, to understand the origins of their motility and functionality in the presence of external stimuli. Then inter-agent communications and agent-environment communications that contribute to the swarm generation are summarized. Furthermore, the swarm behaviors reported to date and the emergence of machine intelligence within these behaviors are reviewed. Eventually, the applications enabled by distinct synthetic swarms are summarized. By discussing the emergent machine intelligence in swarm behaviors, insights are offered into the design and deployment of autonomous synthetic swarms for real-world applications.

Self-driven magnetorobots for recyclable and scalable micro/nanoplastic removal from nonmarine waters

Micro/nanoplastic (MNP) contamination in nonmarine waters has evolved into a notable ecotoxicological threat to the global ecosystem. However, existing strategies for MNP removal are typically limited to chemical flocculation or physical filtering that often fails to decontaminate plastic particulates with ultrasmall sizes or ultralow concentrations. Here, we report a self-driven magnetorobot comprising magnetizable ion-exchange resin sphere that can be used to dynamically remove or separate MNPs from nonmarine waters. As a result of the long-range electrophoretic attraction established by recyclable ion-exchange resin, the magnetorobot shows sustainable removal efficiency of >90% over 100 treatment cycles, with verified broad applicability to varying plastic compositions, sizes, and shapes as well as nonmarine water samples. Our work may facilitate industry-scale MNP removal with affordable cost and minimal secondary pollution and suggests an appealing strategy based on self-propelled micro/nanorobots to sample and assess nanoplastics in aqueous environment.

Beyond Janus Geometry: Characterization of Flow Fields around Nonspherical Photocatalytic Microswimmers

Catalytic microswimmers that move by a phoretic mechanism in response to a self-induced chemical gradient are often obtained by the design of spherical janus microparticles, which suffer from multi-step fabrication and low yields. Approaches that circumvent laborious multi-step fabrication include the exploitation of the possibility of nonuniform catalytic activity along the surface of irregular particle shapes, local excitation or intrinsic asymmetry. Unfortunately, the effects on the generation of motion remain poorly understood. In this work, single crystalline BiVO₄ microswimmers are presented that rely on a strict inherent asymmetry of charge-carrier distribution under illumination. The origin of the asymmetrical flow pattern is elucidated because of the high spatial resolution of measured flow fields around pinned BiVO₄ colloids. As a result the flow from oxidative to reductive particle sides is confirmed. Distribution of oxidation and reduction reactions suggests a dominant self-electrophoretic motion mechanism with a source quadrupole as the origin of the induced flows. It is shown that the symmetry of the flow fields is broken by self-shadowing of the particles and synthetic surface defects that impact the photocatalytic activity of the microswimmers. The results demonstrate the complexity of symmetry breaking in nonspherical microswimmers and emphasize the role of self-shadowing for photocatalytic microswimmers. The findings are leading the way toward understanding of propulsion mechanisms of phoretic colloids of various shapes.

A Critical Review on Nanowire-Motors: Design, Mechanism and Applications

Nanowire-motors (NW-Ms) are promoting the rapid development of emerging biomedicine and environmental governance, and are an important branch of micro-nano motors in the development of nanotechnology. In recent years, huge research breakthroughs have been made in these fields in terms of the fascinating microstructure, conversion efficiency and practical applications of NW-Ms. This review article introduces the latest milestones in NW-Ms research, from production methods, driving mechanisms, control methods to targeted drug delivery, sewage detection, sensors and cell capture. The dynamics and physics of micro-nano devices are reviewed, and finally the current challenges and future research directions in this field are discussed. This review further aims to provide certain guidance for the driving of NW-Ms to meet the urgent needs of emerging applications.

Thermotaxis of Janus particles

The interactions of autonomous microswimmers play an important role for the formation of collective states of motile active matter. We study them in detail for the common microswimmer-design of two-faced Janus spheres with hemispheres made from different materials. Their chemical and physical surface properties may be tailored to fine-tune their mutual attractive, repulsive or aligning behavior. To investigate these effects systematically, we monitor the dynamics of a single gold-capped Janus particle in the external temperature field created by an optically heated metal nanoparticle. We quantify the orientation-dependent repulsion and alignment of the Janus particle and explain it in terms of a simple theoretical model for the induced thermoosmotic surface fluxes. The model reveals that the particle's angular velocity is solely determined by the temperature profile on the equator between the Janus particle's hemispheres and their phoretic mobility contrast. The distortion of the external temperature field by their heterogeneous heat conductivity is moreover shown to break the apparent symmetry of the problem.

Engineering Active Micro and Nanomotors

Micro- and nanomotors (MNMs) are micro/nanoparticles that can perform autonomous motion in complex fluids driven by different power sources. They have been attracting increasing attention due to their great potential in a variety of applications ranging from environmental science to biomedical engineering. Over the past decades, this field has evolved rapidly, with many significant innovations contributed by global researchers. In this review, we first briefly overview the methods used to propel motors and then present the main strategies used to design proper MNMs. Next, we highlight recent fascinating applications of MNMs in two examplary fields, water remediation and biomedical microrobots, and conclude this review with a brief discussion of challenges in the field.

Polarization-density patterns of active particles in motility gradients

The colocalization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. We employ the active-Brownian-particle model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step. Our analysis allows for an optional (but not necessary) orientation-dependent propulsion speed, as often employed in force-free particle steering. The results agree well with measurement data for a thermophoretic microswimmer presented in the companion paper [Söker et al., Phys. Rev. Lett. 126, 228001 (2021)10.1103/PhysRevLett.126.228001], and they can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species "run-and-tumble" model.

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

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

Chemokinesis-driven accumulation of active colloids in low-mobility regions of fuel gradients

Many motile cells exhibit migratory behaviors, such as chemotaxis (motion up or down a chemical gradient) or chemokinesis (dependence of speed on chemical concentration), which enable them to carry out vital functions including immune response, egg fertilization, and predator evasion. These have inspired researchers to develop self-propelled colloidal analogues to biological microswimmers, known as active colloids, that perform similar feats. Here, we study the behavior of half-platinum half-gold (Pt/Au) self-propelled rods in antiparallel gradients of hydrogen peroxide fuel and salt, which tend to increase and decrease the rods' speed, respectively. Brownian Dynamics simulations, a Fokker-Planck theoretical model, and experiments demonstrate that, at steady state, the rods accumulate in low-speed (salt-rich, peroxide-poor) regions not because of chemotaxis, but because of chemokinesis. Chemokinesis is distinct from chemotaxis in that no directional sensing or reorientation capabilities are required. The agreement between simulations, model, and experiments bolsters the role of chemokinesis in this system. This work suggests a novel strategy of exploiting chemokinesis to effect accumulation of motile colloids in desired areas.

Dynamics near planar walls for various model self-phoretic particles

For chemically active particles suspended in a liquid solution and moving by self-phoresis, the dynamics near chemically inert, planar walls is studied theoretically by employing various choices for the activity function, i.e., the spatial distribution of the sites where various chemical reactions take place. We focus on the case of solutions composed of electrically neutral species. This analysis extends previous studies of the case that the chemical activity can be modeled effectively as the release of a "product" molecular species from parts of the surface of the particle by accounting for annihilation of the product molecules by chemical reactions, either on the rest of the surface of the particle or in the volume of the surrounding solution. We show that, for the models considered here, the emergence of "sliding" and "hovering" wall-bound states is a generic, robust feature. However, the details of these states, such as the range of parameters within which they occur, depend on the specific model for the activity function. Additionally, in certain cases there is a reversal of the direction of the motion compared to the one observed if the particle is far away from the wall. We have also studied the changes of the dynamics induced by a direct interaction between the particle and the wall by including a short-ranged repulsive component to the interaction in addition to the steric one (a procedure often employed in numerical simulations of active colloids). Upon increasing the strength of this additional component, while keeping its range fixed, significant qualitative changes occur in the phase portraits of the dynamics near the wall: for sufficiently strong short-ranged repulsion, the sliding steady states of the dynamics are transformed into hovering states. Furthermore, our studies provide evidence for an additional "oscillatory" wall-bound steady state of motion for chemically active particles due to a strong, short-ranged, and direct repulsion. This kind of particle translates along the wall at a distance from it which oscillates between a minimum and a maximum.

Dendritic Janus Nanomotors with Precisely Modulated Coverages and Their Effects on Propulsion

Asymmetric dual-function Janus micro-/nanoparticles (NPs) that have different surface modifications, structures, or material properties are extremely promising as building blocks in constructing micro-/nanomotors. However, current synthesis strategies make it usually difficult to precisely control the percentages of coverages of Janus micro-/NPs, which hinders in-depth research studies of their effects on the performance of Janus nanomotors. This study demonstrates a versatile approach for fabrication of Janus dendritic porous silica nanomotors with precisely modulated coverages from 0 to 100% by controlling the embedded depth of aminopropyl-modified dendritic porous silica NPs (DPSNs-NH₂) with positive charges and subsequently adsorbing the oppositely charged Pt NPs. The diffusion coefficients of DPSNs-NH₂ with different coverages of Pt NPs are systematically investigated. The propulsion can be enhanced by the improvement of catalytic activity of DPSNs, and half-coated DPSNs-NH₂ exhibit highest propulsion among DPSNs-NH₂ with other coverages. More importantly, compared with solid silica nanospheres, the initial increase of the coverage of DPSNs-NH₂ makes more enhancements to the motion performance, which can be used to optimize the relations between the propulsion velocity and loading efficiency of bovine serum albumin. This work paves the way to fabricate tunable multifunctional Janus micro-/nanomotors for future advanced devices.

Toward Understanding of Self-Electrophoretic Propulsion under Realistic Conditions: From Bulk Reactions to Confinement Effects

Active matter concerns itself with the study of particles that convert energy into work, typically motion of the particle itself. This field saw a surge of interest over the past decade, after the first micrometer-sized, man-made chemical motors were created. These particles served as a simple model system for studying in a well-controlled manner complex motion and cooperative behavior as known from biology. In addition, they have stimulated new efforts in understanding out-of-equilibrium statistical physics and started a revolution in microtechnology and robotics. Concentrated effort has gone into realizing these ambitions, and yet much remains unknown about the chemical motors themselves. The original designs for self-propelled particles relied on the conversion of the chemical energy of hydrogen peroxide into motion via catalytic decomposition taking place heterogeneously over the surface of the motor. This sets up gradients of chemical fields around the particle, which allow it to autophorese. That is, the interaction between the motor and the heterogeneously distributed solute species can drive fluid flow and the motor itself. There are two basic designs: the first relies on redox reactions taking place between the two sides of a bimetal, for example, a gold-platinum Janus sphere or nanorod. The second uses a catalytic layer of platinum inhomogeneously vapor-deposited onto a nonreactive particle. For convenience's sake, these can be referred to as redox motors and monometallic half-coated motors, respectively. To date, most researchers continue to rely on variations of these simple, yet elegant designs for their experiments. However, there is ongoing debate on the exact way chemical energy is transduced into motion in these motors. Many of the experimental observations on redox motors were successfully modeled via self-electrophoresis, while for half-coated motors there has been a strong focus on self-diffusiophoresis. Currently, there is mounting evidence that self-electrophoresis provides the dominant contribution to the observed speeds of half-coated motors, even if the vast majority of the reaction products are electroneutral. In this Account, we will summarize the most common electrophoretic propulsion model and discuss its strengths and weaknesses in relation to recent experiments. We will comment on the possible need to go beyond surface reactions and consider the entire medium as an "active fluid" that can create and annihilate charged species. This, together with confinement and collective effects, makes it difficult to gain a detailed understanding of these swimmers. The potentially dominant effect of confinement is highlighted on the basis of a recent study of an electro-osmotic pump that drives fluid along a substrate. Detailed analysis of this system allows for identification of the electro-osmotic driving mechanism, which is powered by micromolar salt concentrations. We will discuss how our latest numerical solver developments, based on the lattice Boltzmann method, should enable us to study collective behavior in systems comprised of these and other electrochemical motors in realistic environments. We conclude with an outlook on the future of modeling chemical motors that may facilitate the community's microtechnological ambitions.

Artificial Chemotaxis of Self-Phoretic Active Colloids: Collective Behavior

Microorganisms use chemotaxis, regulated by internal complex chemical pathways, to swim along chemical gradients to find better living conditions. Artificial microswimmers can mimic such a strategy by a pure physical process called diffusiophoresis, where they drift and orient along the gradient in a chemical density field. Similarly, for other forms of taxis in nature such as photo- or thermotaxis the phoretic counterpart exists. In this Account, we concentrate on the chemotaxis of self-phoretic active colloids. They are driven by self-electro- and diffusiophoresis at the particle surface and thereby acquire a swimming speed. During this process, they also produce nonuniform chemical fields in their surroundings through which they interact with other colloids by translational and rotational diffusiophoresis. In combination with active motion, this gives rise to effective phoretic attraction and repulsion and thereby to diverse emergent collective behavior. A particular appealing example is dynamic clustering in dilute suspensions first reported by a group from Lyon. A subtle balance of attraction and repulsion causes very dynamic clusters, which form and resolve again. This is in stark contrast to the relatively static clusters of motility-induced phase separation at larger densities. To treat chemotaxis in active colloids confined to a plane, we formulate two Langevin equations for position and orientation, which include translational and rotational diffusiophoretic drift velocities. The colloids are chemical sinks and develop their long-range chemical profiles instantaneously. For dense packings, we include screening of the chemical fields. We present a state diagram in the two diffusiophoretic parameters governing translational, as well as rotational, drift and, thereby, explore the full range of phoretic attraction and repulsion. The identified states range from a gaslike phase over dynamic clustering states 1 and 2, which we distinguish through their cluster size distributions, to different types of collapsed states. The latter include a full chemotactic collapse for translational phoretic attraction. Turning it into an effective repulsion, with increasing strength first the collapsed cluster starts to fluctuate at the rim, then oscillates, and ultimately becomes a static collapsed cloud. We also present a state diagram without screening. Finally, we summarize how the famous Keller-Segel model derives from our Langevin equations through a multipole expansion of the full one-particle distribution function in position and orientation. The Keller-Segel model gives a continuum equation for treating chemotaxis of microorganisms on the level of their spatial density. Our theory is extensible to mixtures of active and passive particles and allows to include a dipolar correction to the chemical field resulting from the dipolar symmetry of Janus colloids.

Physico-chemical foundations of particle-laden fluid interfaces

Particle-laden interfaces are ubiquitous nowadays. The understanding of their properties and structure is essential for solving different problems of technological and industrial relevance; e.g. stabilization of foams, emulsions and thin films. These rely on the response of the interface to mechanical perturbations. The complex mechanical response appearing in particle-laden interfaces requires deepening on the understanding of physico-chemical mechanisms underlying the assembly of particles at interface which plays a central role in the distribution of particles at the interface, and in the complex interfacial dynamics appearing in these systems. Therefore, the study of particle-laden interfaces deserves attention to provide a comprehensive explanation on the complex relaxation mechanisms involved in the stabilization of fluid interfaces.

Shape-Directed Microspinners Powered by Ultrasound

The propulsion of micro- and nanoparticles using ultrasound is an attractive strategy for the remote manipulation of colloidal matter using biocompatible energy inputs. However, the physical mechanisms underlying acoustic propulsion are poorly understood, and our ability to transduce acoustic energy into different types of particle motions remains limited. Here, we show that the three-dimensional shape of a colloidal particle can be rationally engineered to direct desired particle motions powered by ultrasound. We investigate the dynamics of gold microplates with twisted star shape ( C _nh symmetry) moving within the nodal plane of a uniform acoustic field at megahertz frequencies. By systematically perturbing the parametric shape of these "spinners", we quantify the relationship between the particle shape and its rotational motion. The experimental observations are reproduced and explained by hydrodynamic simulations that describe the steady streaming flows and particle motions induced by ultrasonic actuation. Our results suggest how particle shape can be used to design colloids capable of increasingly complex motions powered by ultrasound.

Guiding microscale swimmers using teardrop-shaped posts

The swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardrop-shaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardrop-shaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations.

Chemical physics of electroactive materials - the oft-overlooked faces of electrochemistry

Electroactive materials and their applications are enjoying renewed attention, in no small part motivated by the advent of nanoscale tools for their preparation and study. While the fundamentals of charge and mass transport in electrolytes on this scale are by and large well understood, their interplay can have subtle manifestations in the more complex situations typical of, for example, integrated microfluidics-based applications. In particular, the role of faradaic processes is often overlooked or, at best, purposefully suppressed via experimental design. In this introductory article we discuss, using simple illustrations from our laboratories, some of the manifestations of electrochemistry in electroactive materials.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a "swimmer efficiency" functional η is introduced. It is proven that in order to obtain maximum swimmer efficiency, the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.

Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents

Polar solvents like water support the bulk dissociation of themselves and their solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., H₂O₂ ⇌ H⁺ + HO₂^-. Using continuum theory, we study the influence of these association-dissociation reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers). We find that association-dissociation reactions should have a strong influence on swimmers' behaviour, and therefore should be included in future modelling. In particular, such bulk reactions should permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 85, 020401]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely-thin-screening-length approximation used by previous analytical theories. We identify significant departures from this limiting behaviour for micron-sized swimmers under typical experimental conditions and find that the approximation fails entirely for nanoscale swimmers.

Directed Motion of Metallodielectric Particles by Contact Charge Electrophoresis

We investigate the dynamics of metallodielectric Janus particles moving via contact charge electrophoresis (CCEP) between two parallel electrodes. CCEP uses a constant voltage to repeatedly charge and actuate conductive particles within a dielectric fluid, resulting in rapid oscillatory motion between the electrodes. In addition to particle oscillations, we find that micrometer-scale Janus particles move perpendicular to the field at high speeds (up to 600 μm/s) and over large distances. We characterize particle motions and propose a mechanism based on the rotation-induced translation of the particle following charge transfer at the electrode surface. The propulsion mechanism is supported both by experiments with fluorescent particles that reveal their rotational motions and by simulations of CCEP dynamics that capture the relevant electrostatics and hydrodynamics. We also show that interactions among multiple particles can lead to repulsion, attraction, and/or cooperative motions depending on the position and phase of the respective particle oscillators. Our results demonstrate how particle asymmetries can be used to direct the motions of active colloids powered by CCEP.

Catalytic Locomotion of Core-Shell Nanowire Motors

We report Au/Ru core-shell nanowire motors. These nanowires are fabricated using our previously developed electrodeposition-based technique, and their catalytic locomotion in the presence of H₂O₂ is investigated. Unlike conventional bimetallic nanowires that are self-electroosmotically propelled, our open-ended Au/Ru core-shell nanowires show both a noticeable decrease in rotational diffusivity and increase in motor speed with increasing nanowire length. Numerical modeling based on self-electroosmosis attributes decreases in rotational diffusivity to the formation of toroidal vortices at the nanowire tail, but fails to explain the speed increase with length. To reconcile this inconsistency, we propose a combined mechanism of self-diffusiophoresis and electroosmosis based on the oxygen gradient produced by catalytic shells. This mechanism successfully explains not only the speed increase of Au/Ru core-shell nanomotors with increasing length, but also the large variation in speed among Au/Ru, Au/Rh, and Rh/Au core-shell nanomotors. The possible contribution of diffusiophoresis to an otherwise well-established electroosmotic mechanism sheds light on future designs of nanomotors, at the same time highlighting the complex nature of nanoscale propulsion.

Bimetallic Microswimmers Speed Up in Confining Channels

Synthetic microswimmers are envisioned to be useful in numerous applications, many of which occur in tightly confined spaces. It is therefore important to understand how confinement influences swimmer dynamics. Here we study the motility of bimetallic microswimmers in linear and curved channels. Our experiments show swimmer velocities increase, up to 5 times, with the degree of confinement, and the relative velocity increase depends weakly on the fuel concentration and ionic strength in solution. Experimental results are reproduced in a numerical model which attributes the swimmer velocity increase to electrostatic and electrohydrodynamic boundary effects. Our work not only helps to elucidate the confinement effect of phoretic swimmers, but also suggests that spatial confinement may be used as an effective control method for them.

Progress toward Light-Harvesting Self-Electrophoretic Motors: Highly Efficient Bimetallic Nanomotors and Micropumps in Halogen Media

We have developed a highly efficient, bubble-free autonomous nanomotor based on a nanobattery. Bimetallic silver-platinum nanorods are powered by self-electrophoresis and show speeds much higher than those of other electrophoretic motors at similar fuel concentrations. The fuel (I2) can be regenerated by exposure to ambient light, leading to renewed motion of the motor. This versatile system can also be made into a micropump that transports fluid and particles.

Self-Diffusiophoresis of Janus Catalytic Micromotors in Confined Geometries

The self-diffusiophoresis of Janus catalytic micromotors (JCMs) in confined environment is studied using direct numerical simulations. The simulations revealed that, on average, the translocation of a JCM through a short pore is moderately slowed down by the confinement. This slowdown is far weaker compared to the transport of particles through similar pores driven by forces induced by external means or passive diffusiophoresis. Pairing of two JCMs facilitates the translocation of the one JCM entering the pore first but slows down the second JCM. Depending on its initial orientation, a JCM near the entrance of a pore can exhibit different rotational motion, which determines whether it can enter the pore. Once a JCM enters a narrow pore, it can execute a self-alignment process after which it becomes fully aligned with the pore axis and moves to the center line of the pore. Analysis of these results showed that, in addition to hydrodynamic effect, the translation and rotation of JCM is also affected by the "chemical effects", i.e., the modification of the chemical species concentration around a JCM by confining walls and neighboring JCMs. These chemical effects are unique to the self-diffusiophoresis of JCMs and should be considered in design and operations of JCMs in confined environment.

Dynamic self-assembly of microscale rotors and swimmers

Biological systems often involve the self-assembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a well-controlled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components self-assemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micron-scale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial run-and-tumble motion.

Self-Diffusiophoresis of Janus Particles in Near-Critical Mixtures

We theoretically study the self-propulsion of a laser-heated Janus particle in a near-critical water-lutidine mixture, and we relate its velocity v_{p} and squirmer parameter β to the wetting properties of its two hemispheres. For nonionic surface forces, the particle moves the active cap at the front, whereas a charged hydrophilic cap leads to backward motion, in agreement with the experiment. Both v_{p} and β show nonmonotonic dependencies on the heating power, and they may even change sign. The variation of β is expected to strongly affect the collective behavior of dense squirmer systems.

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

The role of hydrazine in mixed fuels (H2O2/N2H4) for Au–Fe/Ni nanomotors

Hydrazine in mixed fuels facilitates the oxidation of H₂O₂ to oxygen bubbles that propel the Au–Fe/Ni nanomotors.

Ionic effects in self-propelled Pt-coated Janus swimmers

Colloidal particles partially coated with platinum and dispersed in H2O2 solution are often used as model self-propelled colloids. Most current data suggest that neutral self-diffusiophoresis propels these particles. However, several studies have shown strong ionic effects in this and related systems, such as a reduction of propulsion speed by salt. We investigate these ionic effects in Pt-coated polystyrene colloids, and find here that the direction of propulsion can be reversed by addition of an ionic surfactant, and that although adding pH neutral salts reduces the propulsion speed, adding the strong base NaOH has little effect. We use these data, as well as measured reaction rates, to argue against propulsion by either neutral or ionic self-diffusiophoresis, and suggest instead that the particle's propulsion mechanism may in fact bear close resemblance to that operative in bimetallic swimmers.

Dynamic clustering and chemotactic collapse of self-phoretic active particles

Recent experiments with self-phoretic particles at low concentrations show a pronounced dynamic clustering [I. Theurkauff et al., Phys. Rev. Lett. 108, 268303 (2012)]. We model this situation by taking into account the translational and rotational diffusiophoretic motion, which the active particles perform in their self-generated chemical field. Our Brownian dynamics simulations show pronounced dynamic clustering only when these two phoretic contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them by power-law-exponential distributions. In case of mere attraction a chemotactic collapse occurs directly from the gaslike into the collapsed state, which we also predict by mapping our Langevin dynamics on the Keller-Segel model for bacterial chemotaxis.

Localized electroosmosis (LEO) induced by spherical colloidal motors

Experimental data show that the speed of colloidal (catalytic) motors decreases as the size of the motor particles increases. However, previous electrokinetic models have shown that the colloidal motor speed for spheres is independent of size, at least for the case of infinitesimally thin double layers and reaction-limited catalysis. Although a size dependence of motor speed has been calculated for diffusion-limited catalysis, most motor experiments are done in the reaction-limited regime. This apparent contradiction led us to examine how motor speed (U) changes with distance (δ) from a wall, starting from the usual electrokinetic equations. A key finding is that interactions between a colloidal motor and a nearby wall produce a localized electroosmotic (LEO) flow field that can significantly alter the motor speed near the wall. Because large motor particles typically settle closer to the wall than small motors, LEO thus provides at least one explanation of the size dependence of motor speed. Furthermore, LEO provides a new method of creating flow fields in capillaries and microchannels.

Nanomotor mechanisms and motive force distributions from nanorotor trajectories

Nanomotors convert chemical energy into mechanical motion. For a given motor type, the underlying chemical reaction that enables motility is typically well known, but the detailed, quantitative mechanism by which this reaction breaks symmetry and converts chemical energy to mechanical motion is often less clear, since it is difficult experimentally to measure important parameters such as the spatial distribution of chemical species around the nanorotor during operation. Without this information on how motor geometry affects motor function, it is difficult to control and optimize nanomotor behavior. Here we demonstrate how one easily observable characteristic of nanomotor operation-the visible trajectory of a nanorotor-can provide quantitative information about the role of asymmetry in nanomotor operation, as well as insights into the spatial distribution of motive force along the surface of the nanomotor, the motive torques, and the effective diffusional motion.

Imaging the proton concentration and mapping the spatial distribution of the electric field of catalytic micropumps

Catalytic engines can use hydrogen peroxide as a chemical fuel in order to drive motion at the microscale. The chemo-mechanical actuation is a complex mechanism based on the interrelation between catalytic reactions and electro-hydrodynamics phenomena. We studied catalytic micropumps using fluorescence confocal microscopy to image the concentration of protons in the liquid. In addition, we measured the motion of particles with different charges in order to map the spatial distributions of the electric field, the electrostatic potential and the fluid flow. The combination of these two techniques allows us to contrast the gradient of the concentration of protons against the spatial variation in the electric field. We present numerical simulations that reproduce the experimental results. Our work sheds light on the interrelation between the different processes at work in the chemomechanical actuation of catalytic pumps. Our experimental approach could be used to study other electrochemical systems with heterogeneous electrodes.