Nonlinear, electrocatalytic swimming in the presence of salt

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

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

Arbitrary Construction of Versatile NIR-Driven Microrobots

Emerging light-driven micro/nanorobots (LMNRs) showcase profound potential for sophisticated manipulation and various applications. However, the realization of a versatile and straightforward fabrication technique remains a challenging pursuit. This study introduces an innovative bulk heterojunction organic semiconductor solar cell (OSC)-based spin-coating approach, aiming to facilitate the arbitrary construction of LMNRs. Leveraging the distinctive properties of a near-infrared (NIR)-responsive organic semiconductor heterojunction solution, this technique enables uniform coating across various dimensional structures (0D, 1D, 2D, 3D) to be LMNRs, denoted as "motorization." The film, with a slender profile measuring ≈140 nm in thickness, effectively preserves the original morphology of objects while imparting actuation capabilities exceeding hundreds of times their own weight. The propelled motion of these microrobots is realized through NIR-driven photoelectrochemical reaction-induced self-diffusiophoresis, showcasing a versatile array of controllable motion profiles. The strategic customization of arbitrary microrobot construction addresses specific applications, ranging from 0D microrobots inducing living crystal formation to intricate, multidimensional structures designed for tasks such as microplastic extraction, cargo delivery, and phototactic precise maneuvers. This study advances user-friendly and versatile LMNR technologies, unlocking new possibilities for various applications, signaling a transformative era in multifunctional micro/nanorobot technologies.

Nonequilibrium Dynamics of Transient Autoelectrophoresis and Effect of Surface Heterogeneity

Nonuniform proton flux around a reactive Janus particle as a result of zone selective heterogeneous surface reaction leads to the formation of asymmetric electrical double layers (EDLs) which assists in generating a proximate electric field dipole around the Janus particle to initiate autoelectrophoretic migration. To estimate the force of the autoelectrophoretic motion of such Janus particles, a mathematical model is set up taking Poisson-Nernst-Plank (PNP) equations coupled with the Navier-Stokes (NS) equations with appropriate boundary conditions. To track the actual motion of these particles, we employ moving deforming mesh and fluid-structure interactions (fsi) of COMSOL Multiphysics while a finite element method is deployed for solving the set of modeled equations. At the outset, transient genesis of the electric field around the particle owing to the nonuniform proton flux has been explored. We further explore the detailed unsteady particle dynamics of the autoelectrophoretic motion with the help of fluid structure interaction physics. It has been observed that the concept of perfect ionic equilibrium in autoelectrophoretic motion is hard to achieve. The autoelectrophoretic particle undergoes continuous change in terms of the ionic concentration around it, speed of the particle, and the transient electric field gradient across the particle. The parametric variation of proton flux reveals that at a relatively lower proton flux a quasi-equilibrium state can be achieved, whereas for higher proton flux the phenomenon can be a pure nonequilibrium case. This parametric study has been done to support the transient dynamics. It has also been shown that the presence of chemical heterogeneity on the particle surface can alter the dynamics of the particle significantly, and the chemical heterogeneity can be used as a tool to control directionality and tuning speed of autoelectrophoretic motion.

Accurate Solutions to Non-Linear PDEs Underlying a Propulsion of Catalytic Microswimmers

Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solution for ion concentration and electric potential in the inner region is known, the electrostatic problem in the outer region was previously solved but only for a linear case. Additionally, only main geometries such as a sphere or cylinder have been favoured. Here, we derive a non-linear outer solution for the electric field and concentrations for swimmers of any shape with given ion surface fluxes that then allow us to find the velocity of particle self-propulsion. The power of our formalism is to include the complicated effects of the anisotropy and inhomogeneity of surface ion fluxes under relevant boundary conditions. This is demonstrated by exact solutions for electric potential profiles in some particular cases with the consequent calculations of self-propulsion velocities.

Electrocatalytic Reaction Driven Flow: Role of pH in Flow Reversal

Immobilized bimetallic structures generate fluid flow during electrocatalytic reactions with hydrogen peroxide, which is typically driven from the anodic metal to the cathodic metal similar to an electroosmotic flow. However, under low reactive regimes, the generated flow becomes fully reversed, which cannot be explained by the classical electroosmotic theory. This work aims at unraveling the origin and dynamics of this flow hysteresis through a combined experimental and numerical approach. The key electrocatalytic parameters that contribute to flow reversal are analyzed experimentally and numerically under low reactive regimes induced by bulk pH variations. The proton gradient that initiates chemomechanical actuation is probed with the use of fluorescence lifetime imaging. The fluid flow dynamics under reactive regimes are visualized by the use of particle tracking. Our numerical simulations elucidate the role of pH variations and additional ionic species (counterions) toward flow reversal. The combination of these techniques highlights the interplay between electrocatalytic and electrokinetic phenomena on the occurrence of flow reversal.

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.

Collective behavior of thermophoretic dimeric active colloids in three-dimensional bulk

Colloids driven by phoresis constitute one of the main avenues for the design of synthetic microswimmers. For these swimmers, the specific form of the phoretic and hydrodynamic interactions dramatically influences their dynamics. Explicit solvent simulations allow the investigation of the different behaviors of dimeric Janus active colloids. The phoretic character is modified from thermophilic to thermophobic, and this, together with the relative size of the beads, strongly influences the resulting solvent velocity fields. Hydrodynamic flows can change from puller-type to pusher-type, although the actual flows significantly differ from these standard flows. Such hydrodynamic interactions combined with phoretic interactions between dimers result in several interesting phenomena in three-dimensional bulk conditions. Thermophilic dimeric swimmers are attracted to each other and form large and stable aggregates. Repulsive phoretic interactions among thermophobic dimeric swimmers hinder such clustering and lead, together with long- and short-ranged attractive hydrodynamic interactions, to short-lived, aligned swarming structures.

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.

Temporal Light Modulation of Photochemically Active, Oscillating Micromotors: Dark Pulses, Mode Switching, and Controlled Clustering

Photochemically powered micromotors are prototype microrobots, and spatiotemporal control is pivotal for a wide range of potential applications. Although their spatial navigation has been extensively studied, temporal control of photoactive micromotors remains much less explored. Using Ag-based oscillating micromotors as a model system, a strategy is presented for the controlled modulation of their individual and collective dynamics via periodically switching illumination on and off. In particular, such temporal light modulation drives individual oscillating micromotors into a total of six regimes of distinct dynamics, as the light-toggling frequencies vary from 0 to 10³ Hz. On an ensemble level, toggling light at 5 Hz gives rise to controlled, reversible clustering of oscillating micromotors and self-assembly of tracer microspheres into colloidal crystals. A qualitative mechanism based on Ag-catalyzed decomposition of H₂O₂ is given to account for some, but not all, of the above observations. This study might potentially inspire more sophisticated temporal control of micromotors and the development of smart, biomimetic materials that respond to environmental stimuli that not only change in space but also in time.

Catalase-linked immunosorbent pressure assay for portable quantitative analysis

In this study, catalase-linked immunosorbent pressure assay with a gas-generation reaction was established for quantitative detection of disease biomarker C-reactive protein (CRP) by a portable pressuremeter. The pressure-based detection system recognizes, transduces, and amplifies the target signal to a convenient target-correlated pressure signal reading in a closed chamber. Biotin molecules were modified on the surface of catalase in order to incorporate catalase into the pressure immunoassay by the streptavidin-biotin interaction. To improve the assay performance, the modification ratios of biotin molecules to catalase, and the concentrations of capture and detection antibodies were further optimized. The catalase-linked immunosorbent pressure assay allows portable and quantitation analysis of CRP with a limit of detection of 1.8 nM, which can satisfy the clinical needs for determining the risk of cardiovascular disease. The catalase-linked immunosorbent pressure assay also shows superior specificity and good accuracy. Compared to the previously reported assay catalyzed by PtNP nanozyme, catalase is not easily deactivated during storage and operation. With the merits of enzymatic efficiency, biocompatibility, low non-specific adsorption and facile modification, catalase can be reasonably used for reproducible, stable, simple quantitative detection of disease markers using a portable pressure-based assay in resource-limited settings.

Fight the flow: the role of shear in artificial rheotaxis for individual and collective motion

To navigate in complex fluid environments, swimming organisms like fish or bacteria often reorient their bodies antiparallel or against the flow, more commonly known as rheotaxis. This reorientation motion enables the organisms to migrate against the fluid flow, as observed in salmon swimming upstream to spawn. Rheotaxis can also be realized in artificial microswimmers - self-propelled particles that mimic swimming microorganisms. Here we study experimentally and by computer simulations the rheotaxis of self-propelled gold-platinum nanorods in microfluidic channels. We observed two distinct modes of artificial rheotaxis: a high shear domain near the bottom wall of the microfluidic channel and a low shear regime in the corners. Reduced fluid drag in the corners promotes the formation of many particle aggregates that rheotax collectively. Our study provides insight into the biomimetic functionality of artificial self-propelled nanorods for dynamic self-assembly and the delivery of payloads to targeted locations.

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.

Effective squirmer models for self-phoretic chemically active spherical colloids

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

Chemically active colloids near osmotic-responsive walls with surface-chemistry gradients

Chemically active colloids move by creating gradients in the composition of the surrounding solution and by exploiting the differences in their interactions with the various molecular species in solution. If such particles move near boundaries, e.g. the walls of the container confining the suspension, gradients in the composition of the solution are also created along the wall. This give rise to chemi-osmosis (via the interactions of the wall with the molecular species forming the solution), which drives flows coupling back to the colloid and thus influences its motility. Employing an approximate 'point-particle' analysis, we show analytically that-owing to this kind of induced active response (chemi-osmosis) of the wall-such chemically active colloids can align with, and follow, gradients in the surface chemistry of the wall. In this sense, these artificial 'swimmers' exhibit a primitive form of thigmotaxis with the meaning of sensing the proximity of a (not necessarily discontinuous) physical change in the environment. We show that the alignment with the surface-chemistry gradient is generic for chemically active colloids as long as they exhibit motility in an unbounded fluid, i.e. this phenomenon does not depend on the exact details of the propulsion mechanism. The results are discussed in the context of simple models of chemical activity, corresponding to Janus particles with 'source' chemical reactions on one half of the surface and either 'inert' or 'sink' reactions over the other half.

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.

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.

Geometrical Performance of Self-Phoretic Colloids and Microswimmers

Within a unified formulation-encompassing self-electrophoresis, self-diffusiophoresis, and self-thermophoresis-we provide a simple integral kernel transforming the relevant surface flux to particle velocity for any spheroid with axisymmetric surface activity and uniform phoretic mobility. Appropriate scaling of the speed allows a dimensionless measure of the motion-producing performance of the motor shape and activity distribution across the surface. For bipartite designs with piecewise uniform flux over complementary surface regions, the performance is mapped out over the entire range of geometry (from discotic through spherical to rodlike shapes) and of bipartitioning, and intermediate aspect ratios that maximize performance are identified. Comparisons are made to experimental data from the literature.

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.

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.

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.

Perspective: nanomotors without moving parts that propel themselves in solution

Self-propelled nanomotors use chemical energy to produce directed motion. Like many molecular motors they suffer strong perturbations from the environment in which they move as a result of thermal fluctuations and do not rely on inertia for their propulsion. Such tiny motors are the subject of considerable research because of their potential applications, and a variety of synthetic motors have been made and are being studied for this purpose. Chemically powered self-propelled nanomotors without moving parts that rely on asymmetric chemical reactions to effect directed motion are the focus of this article. The mechanisms they use for propulsion, how size and fuel sources influence their motion, how they cope with strong molecular fluctuations, and how they behave collectively are described. The practical applications of such nanomotors are largely unrealized and the subject of speculation. Since molecular motors are ubiquitous in biology and perform a myriad of complex tasks, the hope is that synthetic motors might be able to perform analogous tasks. They may have the potential to change our perspective on how chemical dynamics takes place in complex systems.

Diffusive behaviors of circle-swimming motors

Spherical catalytic micromotors fabricated as described in Wheat et al. [Langmuir 26, 13052 (2010)] show fuel concentration dependent translational and rotational velocity. The motors possess short-time and long-time diffusivities that scale with the translational and rotational velocity with respect to fuel concentration. The short-time diffusivities are two to three orders of magnitude larger than the diffusivity of a Brownian sphere of the same size, increase linearly with concentration, and scale as v(2)/2ω. The measured long-time diffusivities are five times lower than the short-time diffusivities, scale as v(2)/{2D(r)[1+(ω/D(r))(2)]}, and exhibit a maximum as a function of concentration. Maximums of effective diffusivity can be achieved when the rotational velocity has a higher order of dependence on the controlling parameter(s), for example fuel concentration, than the translational velocity. A maximum in diffusivity suggests that motors can be separated or concentrated using gradients in fuel concentration. The decrease of diffusivity with time suggests that motors will have a high collision probability in confined spaces and over short times; but will not disperse over relatively long distances and times. The combination of concentration dependent diffusive time scales and nonmonotonic diffusivity of circle-swimming motors suggests that we can expect complex particle responses in confined geometries and in spatially dependent fuel concentration gradients.