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Active matter is an emerging area of interest but the broken symmetry necessary for motion increases the complexity of mathematical modeling. However, these models can be critical for the interpretation of experimental data and efficient optimization of these systems, particularly towards the practical realization of commercial applications. Here, we present a linearized solution (small Péclet and thin-interaction layer) to a generalized mixed boundary-value problem that can be used to describe a variety of active colloidal systems consisting of partially coated (Janus-type) chemically active spherical microparticles, where the size of the active patch is left arbitrary (although axisymmetric). The solution is derived using the Fourier–Legendre-Collocation approach and the accuracy of this methodology is validated against known exact solutions to some limiting cases. We demonstrate the application of the general formulation by solving the mobility of a catalytic "patchy" particle which has two surfaces of differing chemical reactivity which can be characterized by either a fixed-flux or fixed-rate reaction (characterized by an arbitrary Damköhler number (Da)). The analytic solution is shown to agree with limiting cases in the literature presented for both small and infinite Da. Comparison of the different models to experiments published in the literature, indicate that the characterization of the surface reaction by a Dirichlet boundary condition, as in the case of infinite Da is uniquely able to capture the dependence of the mobility on the size of the active patch. This finding highlights the role of mathematical modeling in experimental characterization and optimization of active colloid systems. [ABSTRACT FROM AUTHOR]

Swimming at the microscale typically involves two modes of motion: mechanical propulsion and propulsion due to field interactions. During mechanical propulsion, particles swim by reconfiguring their geometry. When propelled by field interactions, body forces such as phoretic interactions drive mobility. In this work, we employ slender-body theory to explore how a bent rod actuator propels due to a mechanical mode of swimming via hinge articulations and due to a chemical mode of swimming via diffusiophoretic interactions with a solute field. Although previous theoretical studies have examined mechanical and chemical modes of swimming in isolation, the simultaneous investigation of both modes has remained unexplored. For the mechanical mode of swimming, our calculations, both numerical and analytical, recover Purcell’s scallop theorem and show that the bent rod actuator experiences zero net displacement during reciprocal motion. Additionally, we calculate the trajectories traced by a bent rod actuator under a non-reciprocal hinge articulation, revealing that these trajectories are influenced by the amplitude of the hinge articulation, geometric asymmetry, and the angular velocity distribution between the two arms of the bent rod actuator. We provide intuitive explanations for these effects using free-body diagrams. Furthermore, we explore the motion induced by simultaneous hinge articulations and self-diffusiophoresis. We observe that hinge articulations can modify the effective phoretic forces and torques acting on the bent rod actuator, either supporting or impeding propulsion. Additionally, during self-diffusiophoretic propulsion, reciprocal hinge articulations no longer result in zero net displacement. In summary, our findings chart a new direction for designing micron-sized objects that harness both mechanical and chemical modes of propulsion synchronously, offering a mechanism to enact control over trajectories.

The last decade has seen a surge of interest in the field of catalytically propelled micro‐ and nanoswimmers for their potential use in biomedical applications, such as biosensing, biopsy, targeted drug delivery, and on‐the‐fly chemistry. However, to fully utilize these devices, precise control over their motion is essential. Therefore, it is important to thoroughly understand their locomotion mechanisms. Herein, the currently accepted mechanisms for propulsion are discussed, which are self‐electrophoresis, self‐diffusiophoresis, and bubble recoil. Additionally, the concept of using multilocomotive mechanisms as a solution to achieve fully autonomous navigation is explored. Moreover, recent advances in the design of these devices are explored. [ABSTRACT FROM AUTHOR]

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation. [ABSTRACT FROM AUTHOR]

The last decade has seen a surge of interest in the field of catalytically propelled micro‐ and nanoswimmers for their potential use in biomedical applications, such as biosensing, biopsy, targeted drug delivery, and on‐the‐fly chemistry. However, to fully utilize these devices, precise control over their motion is essential. Therefore, it is important to thoroughly understand their locomotion mechanisms. Herein, the currently accepted mechanisms for propulsion are discussed, which are self‐electrophoresis, self‐diffusiophoresis, and bubble recoil. Additionally, the concept of using multilocomotive mechanisms as a solution to achieve fully autonomous navigation is explored. Moreover, recent advances in the design of these devices are explored.

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation.

Understanding and controlling the swimming direction of a synthetic nano‐ and micromotor holds fundamental and applied significance. Here, we focus on platinum‐containing Janus colloids that catalytically decompose H2O2 into O2, an archetypical model of chemical micromotor. We discover that platinum oxides (primarily PtO) are produced on Pt films sputter‐coated in O2 plasma, and PtO reverses the motor possibly by self‐electrophoresis. Using this knowledge, micromotors moving in either direction were fabricated by intentionally introducing or removing PtO. These findings challenge the conventional wisdom that a Pt micromotor is powered by Pt alone, and open up new avenues for controlling the swimming directions of a micro‐ and nanomachine. [ABSTRACT FROM AUTHOR]

Distinguishing the operating mechanisms of nano‐ and micromotors powered by chemical gradients, i.e. "autophoresis", holds the key for fundamental and applied reasons. In this article, we propose and experimentally confirm that the speeds of a self‐diffusiophoretic colloidal motor scale inversely to its population density but not for self‐electrophoretic motors, because the former is an ion source and thus increases the solution ionic strength over time while the latter does not. They also form clusters in visually distinguishable and quantifiable ways. This pair of rules is simple, powerful, and insensitive to the specific material composition, shape or size of a colloidal motor, and does not require any measurement beyond typical microscopy. These rules are not only useful in clarifying the operating mechanisms of typical autophoretic micromotors, but also in predicting the dynamics of unconventional ones that are yet to be experimentally realized, even those involving enzymes. [ABSTRACT FROM AUTHOR]

Ultrasmall nanomotors (<100 nm) are highly desirable nanomachines for their size-specific advantages over their larger counterparts in applications spanning nanomedicine, directed assembly, active sensing, and environmental remediation. While there are extensive studies on motors larger than 100 nm, the design and understanding of ultrasmall nanomotors have been scant due to the lack of high-resolution imaging of their propelled motions with orientation and shape details resolved. Here, we report the imaging of the propelled motions of catalytically powered ultrasmall nanomotors─hundreds of them─at the nanometer resolution using liquid-phase transmission electron microscopy. These nanomotors are Pt nanoparticles of asymmetric shapes ("tadpoles" and "boomerangs"), which are colloidally synthesized and observed to be fueled by the catalyzed decomposition of NaBH 4 in solution. Statistical analysis of the orientation and position trajectories of fueled and unfueled motors, coupled with finite element simulation, reveals that the shape asymmetry alone is sufficient to induce local chemical concentration gradient and self-diffusiophoresis to act against random Brownian motion. Our work elucidates the colloidal design and fundamental forces involved in the motions of ultrasmall nanomotors, which hold promise as active nanomachines to perform tasks in confined environments such as drug delivery and chemical sensing.

In nature, microorganisms could sense the intensity of the incident visible light and exhibit bidirectional (positive or negative) phototaxis. However, it is still challenging to achieve the similar biomimetic phototaxis for the artificial micro/nanomotor (MNM) counterparts with the size from a few nanometers to a few micrometers. In this work, we report a fuel-free carbon nitride (C3N4)/ polypyrrole nanoparticle (PPyNP)-based smart MNM operating in water, whose behavior resembles that of the phototactic microorganism. The MNM moves toward the visible light source under low illumination and away from it under high irradiation, which relies on the competitive interplay between the light-induced selfdiffusiophoresis and self-thermophoresis mechanisms concurrently integrated into the MNM. Interestingly, the competition between these two mechanisms leads to a collective bidirectional phototaxis of an ensemble of MNMs under uniform illuminations and a spinning schooling behavior under a nonuniform light, both of which can be finely controllable by visible light energy. Our results provide important insights into the design of the artificial counterpart of the phototactic microorganism with sophisticated motion behaviors for diverse applications. [ABSTRACT FROM AUTHOR]

Recently, organometallic halide perovskites (OMHPs) have attracted significant attention due to their high light absorption coefficient, high charge carrier mobility, and long carrier lifetime. One of the key shortcomings of the OMHP device application is its poor stability under humid conditions. Thus, it is important to study the relationship between humidity and OMHP crystals in their thin films. In this work, the large‐scale movement behavior of CH3NH3PbI3‐xClx crystals in their films is discovered. It is concluded that the number of moving CH3NH3PbI3‐xClx crystals can be controlled by the humidity of the external environment. The movement behavior of the perovskite grains is attributed to the asymmetric decomposition of perovskite under high relative humidity (RH) conditions. [ABSTRACT FROM AUTHOR]

Nanomotors in solution have many potential applications. However, it has been a significant challenge to realize the directional motion of nanomotors. Here, we report cadmium chloride tetrahydrate (CdCl 2 ·4H 2 O) nanomotors with remarkable directional movement under electron beam irradiation. Using in situ liquid phase transmission electron microscopy, we show that the CdCl 2 ·4H 2 O nanoparticle with asymmetric surface facets moves through the liquid with the flat end in the direction of motion. As the nanomotor morphology changes, the speed of movement also changes. Finite element simulation of the electric field and fluid velocity distribution around the nanomotor assists the understanding of ionic self-diffusiophoresis as a driving force for the nanomotor movement; the nanomotor generates its own local ion concentration gradient due to different chemical reactivities on different facets.

While chemical communication plays a key role in diverse natural processes, the intelligent chemical communication between synthetic nanomotors remains unexplored. The design and operation of bioinspired synthetic nanomotors is presented. Chemical communication between nanomotors is possible and has an influence on propulsion behavior. A chemical 'message' is sent from a moving activator motor to a nearby activated (receiver) motor by release of Ag+ ions from a Janus polystyrene/Ni/Au/Ag activator motor to the activated Janus SiO2/Pt nanomotor. The transmitted silver signal is translated rapidly into a dramatic speed change associated with the enhanced catalytic activity of activated motors. Selective and successive activation of multiple nanomotors is achieved by sequential localized chemical communications. The concept of establishing chemical communication between different synthetic nanomotors paves the way to intelligent nanoscale robotic systems that are capable of cooperating with each other. [ABSTRACT FROM AUTHOR]

The double-faced Janus micro-motor, which utilizes the heterogeneity between its two hemispheres to generate self-propulsion, has shown great potential in water cleaning, drug delivery in micro/nanofluidics, and provision of power for a novel micro-robot. In this paper, we focus on the self-propulsion of a platinum-silica (Pt-SiO2) spherical Janus micro-motor (JM), which is one of the simplest micro-motors, suspended in a hydrogen peroxide solution (H2O2). Due to the catalytic decomposition of H2O2 on the Pt side, the JM is propelled by the established concentration gradient known as diffusoiphoretic motion. Furthermore, as the JM size increases to O (10 m), oxygen molecules nucleate on the Pt surface, forming microbubbles. In this case, a fast bubble propulsion is realized by the microbubble cavitation-induced jet flow. We systematically review the results of the above two distinct mechanisms: self-diffusiophoresis and microbubble propulsion. Their typical behaviors are demonstrated, based mainly on experimental observations. The theoretical description and the numerical approach are also introduced. We show that this tiny motor, though it has a very simple structure, relies on sophisticated physical principles and can be used to fulfill many novel functions. [ABSTRACT FROM AUTHOR]

Self-phoretic chemically active Janus particles move by inducing—via non-equilibrium chemical reactions occurring on their surfaces—changes in the chemical composition of the solution in which they are immersed. This process leads to gradients in chemical composition along the surface of the particle, as well as along any nearby boundaries, including solid walls. Chemical gradients along a wall can give rise to chemi-osmosis, i.e., the gradients drive surface flows which, in turn, drive flow in the volume of the solution. This bulk flow couples back to the particle, and thus contributes to its self-motility. Since chemi-osmosis strongly depends on the molecular interactions between the diffusing molecular species and the wall, the response flow induced and experienced by a particle encodes information about any chemical patterning of the wall. Here, we extend previous studies on self-phoresis of a sphere near a chemically patterned wall to the case of particles with rod-like, elongated shape. We focus our analysis on the new phenomenology potentially emerging from the coupling—which is inoperative for a spherical shape—of the elongated particle to the strain rate tensor of the chemi-osmotic flow. Via detailed numerical calculations, we show that the dynamics of a rod-like particle exhibits a novel ‘edge-following’ steady state: the particle translates along the edge of a chemical step at a steady distance from the step and with a steady orientation. Moreover, within a certain range of system parameters, the edge-following state co-exists with a ‘docking’ state (the particle stops at the step, oriented perpendicular to the step edge), i.e., a bistable dynamics occurs. These findings are rationalized as a consequence of the competition between the fluid vorticity and the rate of strain by using analytical theory based on the point-particle approximation which captures quasi-quantitatively the dynamics of the system.

Self-propelled droplets are a class of active matter systems composed of one fluid dispersed in another immiscible fluid. Despite the inherent spherical symmetry in the initial droplet shape and composition, self-propulsion in these systems is achieved by a spontaneous symmetry-breaking bifurcation. Either a chemical reaction, micelle-induced solubilization, or a phase transition may induce gradients in the interfacial tension, generating a Marangoni convection and thereby resulting in self-propulsion. The simplicity associated with these self-propelled droplet systems makes them excellent candidates for investigating the solitary and collective behaviour of several biological swimmers, ranging from single-celled bacteria to school of fishes. Additionally, due to their tunable mobility characteristics, these swimmers have immense potential as smart materials designed to execute intricate tasks in microscopic domains. In this review, we present state-of-the-art experimental and theoretical research relevant to self-propelled swimming droplets. [Display omitted] [ABSTRACT FROM AUTHOR]

Asymmetric modification with an enzyme confers nanorods an enhanced diffusive motion that is dependent on the concentration of the enzyme substrate. In turn, such a motion opens the possibility of determining the concentration of the enzyme substrate by measuring the diffusion coefficient of nanorods modified with the appropriate enzyme. Nanorods, with a Pt and a polypyrrole (PPy) segment, were fabricated. The PPy segment of such nanorods was then modified with glucose oxidase (GOx), glutamate oxidase (GluOx), or xanthine oxidase (XOD). Calibration curves, linking the diffusion coefficient of the oxidase-modified nanorods to the concentration of the oxidase substrate, were subsequently built. The oxidase-modified nanorods and their calibration curves were finally used to determine substrate concentrations both in simple aqueous solutions and in complex samples such as horse serum and cell culture media. Based on the obtained results we are confident that our motion-based approach to sensing can be developed to the point where different nanorods in a mixture simultaneously report on the concentration of different compounds with good temporal and spatial resolution. [ABSTRACT FROM AUTHOR]

Highlights: [•] Autonomous nano- and micromotors are particles that convert energy locally through symmetry breaking. [•] These motors operate in the low Reynolds number regime through several propulsion mechanisms. [•] Functionality such as steering and cargo pick up/delivery can be incorporated into micromotors. [•] Synthetic motors exhibit collective behavior that is mimetic of living microorganisms. [•] Several applications are emerging in biochemical analysis, microfluidic pumping, particle sorting, and assembly. [ABSTRACT FROM AUTHOR]

2D transition-metal-dichalcogenide materials, such as molybdenum disulfide (MoS 2 ) have received immense interest owing to their remarkable structure-endowed electronic, catalytic, and mechanical properties for applications in optoelectronics, energy storage, and wearable devices. However, 2D materials have been rarely explored in the field of micro/nanomachines, motors, and robots. Here, MoS 2  with anatase TiO 2  is successfully integrated into an original one-side-open hollow micromachine, which demonstrates increased light absorption of TiO 2 -based micromachines to the visible region and the first observed motion acceleration in response to ionic media. Both experimentation and theoretical analysis suggest the unique type-II bandgap alignment of MoS 2 /TiO 2  heterojunction that accounts for the observed unique locomotion owing to a competing propulsion mechanism. Furthermore, by leveraging the chemical properties of MoS 2 /TiO 2 , the micromachines achieve sunlight-powered water disinfection with 99.999% Escherichia coli lysed in an hour. This research suggests abundant opportunities offered by 2D materials in the creation of a new class of micro/nanomachines and robots., (© 2022 Wiley-VCH GmbH.)

In nature, microorganisms could sense the intensity of the incident visible light and exhibit bidirectional (positive or negative) phototaxis. However, it is still challenging to achieve the similar biomimetic phototaxis for the artificial micro/nanomotor (MNM) counterparts with the size from a few nanometers to a few micrometers. In this work, we report a fuel-free carbon nitride (C 3 N 4 )/polypyrrole nanoparticle (PPyNP)-based smart MNM operating in water, whose behavior resembles that of the phototactic microorganism. The MNM moves toward the visible light source under low illumination and away from it under high irradiation, which relies on the competitive interplay between the light-induced self-diffusiophoresis and self-thermophoresis mechanisms concurrently integrated into the MNM. Interestingly, the competition between these two mechanisms leads to a collective bidirectional phototaxis of an ensemble of MNMs under uniform illuminations and a spinning schooling behavior under a nonuniform light, both of which can be finely controllable by visible light energy. Our results provide important insights into the design of the artificial counterpart of the phototactic microorganism with sophisticated motion behaviors for diverse applications., Competing Interests: The authors declare no competing interest.

Micro/nanomotors have achieved huge progress in driving power divergence and accurate maneuver manipulations in the last two decades. However, there are still several obstacles to the potential biomedical applications, with respect to their biotoxicity and biocompatibility. Gallium- and indium-based liquid metal (LM) alloys are outstanding candidates for solving these issues due to their good biocompatibility and low biotoxicity. Hereby, we fabricate LM Janus micromotors (LMJMs) through ultrasonically dispersing GaInSn LM into microparticles and sputtering different materials as demanded to tune their moving performance. These LMJMs can move in alkaline solution due to the reaction between Ga and NaOH. There are two driving mechanisms when sputtering materials are metallic or nonmetallic. One is self-electrophoresis when sputtering materials are metallic, and the other one is self-diffusiophoresis when sputtering materials are nonmetallic. Our LMJMs can flip between those two modes by varying the deposited materials. The self-electrophoresis-driven LMJMs' moving speed is much faster than the self-diffusiophoresis-driven LMJMs' speed. The reason is that the former occurs galvanic corrosion reaction, while the latter is correlated to chemical corrosion reaction. The switching of the driving mechanism of the LMJMs can be used to fit into different biochemical application scenarios.

One of the recent frontiers of nanotechnology research involves machines that operate at nano- and microscales, also known as nano/micromotors. Their potential applications in biomedicine, environmental sciences and engineering, military and defense industries, self-assembly, and many other areas have fueled an intense interest in this topic over the last 15 years. Despite deepened understanding of their propulsion mechanisms, we are still in the early days of exploring the dynamics of micromotors in complex and more realistic environments. Confinements, as a typical example of complex environments, are extremely relevant to the applications of micromotors, which are expected to travel in mucus gels, blood vessels, reproductive and digestive tracts, microfluidic chips, and capillary tubes. In this review, we summarize and critically examine recent studies (mostly experimental ones) of micromotor dynamics in confinements in 3D (spheres and porous network, channels, grooves, steps, and obstacles), 2D (liquid-liquid, liquid-solid, and liquid-air interfaces), and 1D (chains). In addition, studies of micromotors moving in the bulk solution and the usefulness of acoustic levitation is discussed. At the end of this article, we summarize how confinements can affect micromotors and offer our insights on future research directions. This review article is relevant to readers who are interested in the interactions of materials with interfaces and structures at the microscale and helpful for the design of smart and multifunctional materials for various applications.

A novel light-driven Au-WO 3 @C Janus micromotor based on colloidal carbon WO 3 nanoparticle composite spheres (WO 3 @C) prepared by one-step hydrothermal treatment is described. The Janus micromotors can move in aqueous media at a speed of 16 μm/s under 40 mW/cm 2 UV light due to diffusiophoretic effects. The propulsion of such Au-WO 3 @C Janus micromotors (diameter ∼ 1.0 μm) can be generated by UV light in pure water without any external chemical fuels and readily modulated by light intensity. After depositing a paramagnetic Ni layer between the Au layer and WO 3 , the motion direction of the micromotor can be precisely controlled by an external magnetic field. Such magnetic micromotors not only facilitate recycling of motors but also promise more possibility of practical applications in the future. Moreover, the Au-WO 3 @C Janus micromotors show high sensitivity toward extremely low concentrations of sodium-2,6-dichloroindophenol (DCIP) and Rhodamine B (RhB). The moving speed of motors can be significantly accelerated to 26 and 29 μm/s in 5 × 10 -4 wt % DCIP and 5 × 10 -7 wt % RhB aqueous solutions, respectively, due to the enhanced diffusiophoretic effect, which results from the rapid photocatalytic degradation of DCIP and RhB by WO 3 . This photocatalytic acceleration of the Au-WO 3 @C Janus micromotors confirms the self-diffusiophoretic mechanism and opens an opportunity to tune the motility of the motors. This work also offers the light-driven micromotors a considerable potential for detection and rapid photodegradation of dye pollutants in water.

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 H 2 O 2 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.