Optimal run-and-tumble-based transportation of a Janus particle with active steering

Run-and-tumble kinematics of Enterobacter Sp. SM3

The recent discovery of the peritrichous, swarm-competent bacterium Enterobacter sp. SM3 has offered a new opportunity to investigate the connection between bacterial swimming and swarming. Here, we report the run-and-tumble behavior of SM3 as planktonic swimming cells and as swarming cells diluted in liquid medium, drawing comparison between the two states. Swimming cells of SM3 run for an average of 0.77 s with a speed of approximately 30µm/s before tumbling. Tumbles last for a duration of 0.12 s on average and cause changes in direction averaging 69^{∘}. Swimming cells exposed to the common chemoattractant serine in bulk solution suppress the frequency of tumbles in the steady state, lengthening the average run duration and decreasing the average tumble angle. When exposed to aspartate, cells do not demonstrate a notable change in run-and-tumble parameters in the steady state. For swarming cells of SM3, the frequency of tumbles is reduced, with the average run duration being 50% longer on average than that of swimming cells in the same liquid medium. Additionally, the average tumble angle of swarming cells is smaller by 35%. These findings reveal that the newly identified species, SM3, performs run-and-tumble motility similar to other species of peritrichous bacteria such as E. coli, both in the swimming and swarming states. We present a simple mechanical model, which provides a physical understanding of the run-and-tumble behavior of peritrichous bacteria.

Enhanced emulsification performance and interfacial properties of Janus-like rapeseed cruciferin through asymmetric acylation modification

Plant protein emulsifiers, particularly rapeseed protein isolate with its superior amino acid composition and predominantly globular protein, have captured significant interest in the food industry. Nonetheless, the application of these proteins has been stymied by their lackluster emulsification properties. Addressing this challenge, our study implements an innovative asymmetric acylation technique to modify the surface of rapeseed cruciferin (RC), morphing it into a structure resembling Janus nanoparticles. This alteration amplifies the emulsification prowess of RC by a remarkable 2.7 times compared to its natural form, and 1.43 times over its conventionally acylated counterpart. The asymmetrically acylated RC, marked by a distinctive three-phase contact angle of 90.4°, manifests an outstanding amphiphilic character. Moreover, it surpasses both the natural and conventionally acylated RC in terms of diffusion, penetration, and rearrangement rates, as well as protein concentration at the oil-water interface. Compared to commonly used emulsifiers in the food industry, such as lecithin and soy protein, the asymmetrically acylated RC stands out, stabilizing emulsions with the tiniest particle size and effectively staving off emulsion stratification over a longer duration. This study underscores that asymmetric acylation serves as a reliable methodology for producing efficient plant protein emulsifiers, considerably amplifying their utility in the food industry.

Efficient control protocols for an active Ornstein-Uhlenbeck particle

Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find that protocols designed to minimize the excess work (up to linear response) perform better than naive protocols with constant velocity for a wide range of protocol durations.

Inverted Sedimentation of Active Particles in Unbiased ac Fields

Gaining control over the motion of active particles is crucial for applications ranging from targeted cargo delivery to nanomedicine. While much progress has been made recently to control active motion based on external forces, flows, or gradients in concentration or light intensity, which all have a well-defined direction or bias, little is known about how to steer active particles in situations where no permanent bias can be realized. Here, we show that ac fields with a vanishing time average provide an alternative route to steering active particles. We exemplify this route for inertial active particles in a gravitational field, observing that a substantial fraction of them persistently travels in the upward direction upon switching on the ac field, resulting in an inverted sedimentation profile at the top wall of a confining container. Our results offer a generic control principle that could be used in the future to steer active motion, direct collective behaviors, and purify mixtures.

Ultrasonic Steering Wheels: Turning Micromotors by Localized Acoustic Microstreaming

The ability to steer micromotors in specific directions and at precise speeds is highly desired for their use in complex environments. However, a generic steering strategy that can be applied to micromotors of all types and surface coatings is yet to be developed. Here, we report that ultrasound of ∼100 kHz can spin a spherical micromotor so that it turns left or right when moving forward, or that it moves in full circles. The direction and angular speeds of their spinning and the radii of circular trajectories are precisely tunable by varying ultrasound voltages and frequencies, as well as particle properties such as its radius, materials, and coating thickness. Such spinning is hypothesized to originate from the circular microstreaming flows localized around a solid microsphere vibrating in ultrasound. In addition to causing a micromotor to spin, such streaming flows also helped release cargos from a micromotor during a capture-transport-release mission. Localized microstreaming does not depend on or interference with a specific propulsion mechanism and can steer a wide variety of micromotors. This work suggests that ultrasound can be used to steer microrobots in complex, biologically relevant environments as well as to steer microorganisms and cells.

3D-printed microrobots from design to translation

Microrobots have attracted the attention of scientists owing to their unique features to accomplish tasks in hard-to-reach sites in the human body. Microrobots can be precisely actuated and maneuvered individually or in a swarm for cargo delivery, sampling, surgery, and imaging applications. In addition, microrobots have found applications in the environmental sector (e.g., water treatment). Besides, recent advancements of three-dimensional (3D) printers have enabled the high-resolution fabrication of microrobots with a faster design-production turnaround time for users with limited micromanufacturing skills. Here, the latest end applications of 3D printed microrobots are reviewed (ranging from environmental to biomedical applications) along with a brief discussion over the feasible actuation methods (e.g., on- and off-board), and practical 3D printing technologies for microrobot fabrication. In addition, as a future perspective, we discussed the potential advantages of integration of microrobots with smart materials, and conceivable benefits of implementation of artificial intelligence (AI), as well as physical intelligence (PI). Moreover, in order to facilitate bench-to-bedside translation of microrobots, current challenges impeding clinical translation of microrobots are elaborated, including entry obstacles (e.g., immune system attacks) and cumbersome standard test procedures to ensure biocompatibility.

Microbots have attracted attention due to an ability to reach places and perform tasks which are not possible with conventional techniques in a wide range of applications. Here, the authors review the recent work in the field on the fabrication, application and actuation of 3D printed microbots offering a view of the direction of future microbot research.

pH-Sensitive Controlled Motion of Micrometer-sized Oil Droplets in a Solution of Surfactants Containing Fumaric Acid Derivatives

Self-propelled droplets are of considerable interest as an appropriate model for understanding the self-propulsion of objects in the fields of nonequilibrium physics and nonlinear science. Several research groups have reported the monodirectional motion of droplets, that is, chemotaxis, using stimuli-responsive materials. However, the precise control of chemotaxis remains challenging from the perspective of synthetic chemistry because chemotactic motion is primarily induced by the consumption of reactive oil or surfactants. Herein, we report a chemical system containing pH-responsive fumaric acid derivatives, in which the oil droplet exhibited positive chemotaxis over a wide pH range-from basic to acidic conditions. From the measurements of the interfacial tension between the oil and aqueous phases, it was deduced that the positive chemotaxis was due to heterogeneity in the interfacial tension of the droplet surface, which was accompanied by the production of surface-active compounds in the pH gradient in a linear-type channel.

Programmable Multimodal Optothermal Manipulation of Synthetic Particles and Biological Cells

Optical manipulation of tiny objects has benefited many research areas ranging from physics to biology to micro/nanorobotics. However, limited manipulation modes, intense lasers with complex optics, and applicability to limited materials and geometries of objects restrict the broader uses of conventional optical tweezers. Herein, we develop an optothermal platform that enables the versatile manipulation of synthetic micro/nanoparticles and live cells using an ultralow-power laser beam and a simple optical setup. Five working modes (i.e., printing, tweezing, rotating, rolling, and shooting) have been achieved and can be switched on demand through computer programming. By incorporating a feedback control system into the platform, we realize programmable multimodal control of micro/nanoparticles, enabling autonomous micro/nanorobots in complex environments. Moreover, we demonstrate in situ three-dimensional single-cell surface characterizations through the multimodal optothermal manipulation of live cells. This programmable multimodal optothermal platform will contribute to diverse fundamental studies and applications in cellular biology, nanotechnology, robotics, and photonics.

The role of particle-electrode wall interactions in mobility of active Janus particles driven by electric fields

HYPOTHESIS

The interaction of active particles with walls can explain discrepancies between experiments and theory derived for particles in the bulk. For an electric field driven metallodielectric Janus particle (JP) adjacent to an electrode, interaction between the asymmetric particle and the partially screened electrode yields a net electrostatic force - termed self-dielectrophoresis (sDEP) - that competes with induced-charge electrophoresis (ICEP) to reverse particle direction.

EXPERIMENTS

The potential contribution of hydrodynamic flow to the reversal is evaluated by visualizing flow around a translating particle via micro-particle image velocimetry and chemically suppressing ICEP with poly(l-lysine)-g-poly(ethylene glycol) (PLL-PEG). Mobility of Polystyrene-Gold JPs is measured in KCl electrolytes of varying concentration and with a capacitive SiO₂ coating at the metallic JP surface or electrode. Results are compared with theory and numerical simulations accounting for electrode screening.

FINDINGS

PLL-PEG predominantly suppresses low-frequency mobility where propulsive electro-hydrodynamic jetting is observed; supporting the hypothesis of an electrostatic driving force at high frequencies. Simulations and theory show the magnitude, direction and frequency dispersion of JP mobility are obtained by superposition of ICEP and sDEP using the JP height and capacitance as fitting parameters. Wall proximity enhances ICEP and sDEP and manifests a secondary ICEP charge relaxation time dominating in the contact limit.

Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers

We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. The agreement between results from theory and simulations is found to be good.

Emergence of Colloidal Patterns in ac Electric Fields

Suspended microparticles subjected to ac electrical fields collectively organize into band patterns perpendicular to the field direction. The bands further develop into zigzag shaped patterns, in which the particles are observed to circulate. We demonstrate that this phenomenon can be observed quite generically by generating such patterns with a wide range of particles: silica spheres, fatty acid, oil, and coacervate droplets, bacteria, and ground coffee. We show that the phenomenon can be well understood in terms of second order electrokinetic flow, which correctly predicts the hydrodynamic interactions required for the pattern formation process. Brownian particle simulations based on these interactions accurately recapitulate all of the observed pattern formation and symmetry-breaking events, starting from a homogeneous particle suspension. The emergence of the formed patterns can be predicted quantitatively within a parameter-free theory.

Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles

One of the most intriguing phenomena in active matter has been the gas-liquid-like motility-induced phase separation (MIPS) observed in repulsive active particles. However, experimentally, no particle can be a perfect sphere, and the asymmetric shape, mass distribution, or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The nonvanishing current in non-equilibrium steady states microscopically originates from the motility "relieved" by automatic rotation, which breaks the detailed balance at the continuum level. This suggests that no equilibrium-like phase separation theory can be constructed for chiral active colloids even with tiny active torque, in which no visible collective motion exists. This mechanism also sheds light on the understanding of dynamic clusters observed in a variety of active matter systems.

A geometric criterion for the optimal spreading of active polymers in porous media

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

Electric polarizability of metallodielectric Janus particles in electrolyte solutions

Metallodielectric Janus particles (JPs) and electric fields have been a useful combination for the development of innovative concepts on AC electrokinetics, directed transport and collective dynamics. The polarizability, and its frequency dependence, underlie the rich behavior exhibited by JPs. Nonetheless, direct measurements of polarizability are few and the interplay of different mechanisms remains unclear. This paper discusses measurements and strategies to tailor the magnitude of the polarizability of JPs. Our approach uses electrorotation to measure the polarizability of particles with different thicknesses of metal in electrolyte solutions. On the other hand, we gain further insight into the basic polarization mechanisms through modeling based on the fundamental transport equations. JPs exhibit rich polarization spectra that depend strongly on the thickness of the metal layer, the conductivity of the medium and the surface charge. At low frequencies-around 10 kHz-the results indicate that counter-field rotation stems from the charging of the double layer at the particle-electrolyte interface, while the transition to co-field rotation at high frequencies (above 100 kHz) stems from the Maxwell-Wagner relaxation. The latter polarization mechanism is significantly affected by the conductivity within the electrical double layer. The insights from this study provide helpful quantitative information for the design of colloidal machines with desirable features such as targeted propulsion, and tunable collective dynamics.

Rational Design of Self-Propelling Particles for Unified Cargo Loading and Transportation

Recent studies on electrically powered active particles that can both self-propel and manipulate cargo load and release, have focused on both spherically shaped Janus particles (JP) and on a parallel electrically conducting plates setup. Yet, spherically shaped JPs set a geometrical limitation on the ability to smartly design multiple dielectrophoretic traps on a single active particle. Herein, these active carriers are extended to accommodate any desired shape and selective metallic coating, using a standard photolithography method. The resulting designed positive and negative dielectrophoretic traps of controlled size, location, and intensity, performed as sophisticated active carriers with a high level of control over their mobility and cargo loading. In addition to cargo loading, the engineered particles exhibit interesting motion in an electrically insulating substrate setup, with in-plane electric field, and, in particular, a tilt angle, and even flipping, that strongly depended on the field frequency and amplitude, hence, exhibiting a much more diverse and rich behavior than spherical JP. The engineered self-propelling carriers are expected to open up new possibilities for unified, label-free and selective cargo loading, transport, and delivery of complex multi-particles.

Light-Driven Magnetic Encoding for Hybrid Magnetic Micromachines

Remote manipulation of a micromachine under an external magnetic field is significant in a variety of applications. However, magnetic manipulation requires that either the target objects or the fluids should be ferromagnetic or superparamagnetic. To extend the applicability, we propose a versatile optical printing technique termed femtosecond laser-directed bubble microprinting (FsLDBM) for on-demand magnetic encoding. Harnessing Marangoni convection, evaporation flow, and capillary force for long-distance delivery, near-field attraction, and printing, respectively, FsLDBM is capable of printing nanomaterials on the solid-state substrate made of arbitrary materials. As a proof-of-concept, we actuate a 3D polymer microturbine under a rotating magnetic field by implementing γ-Fe₂O₃ nanomagnets on its blade. Moreover, we demonstrate the magnetic encoding on a living daphnia and versatile manipulation of the hybrid daphnia. With its general applicability, the FsLDBM approach provides opportunities for magnetic control of general microstructures in a variety of applications, such as smart microbots and biological microsurgery.

Pair correlation of dilute active Brownian particles: From low-activity dipolar correction to high-activity algebraic depletion wings

We study the pair correlation of active Brownian particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: While particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity, where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.

Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles

We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized ‘standard’ model (Poisson–Nernst–Planck formulation) and on the assumptions of a ‘weak’ field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Opto-thermoelectric microswimmers

Inspired by the "run-and-tumble" behaviours of Escherichia coli (E. coli) cells, we develop opto-thermoelectric microswimmers. The microswimmers are based on dielectric-Au Janus particles driven by a self-sustained electrical field that arises from the asymmetric optothermal response of the particles. Upon illumination by a defocused laser beam, the Janus particles exhibit an optically generated temperature gradient along the particle surfaces, leading to an opto-thermoelectrical field that propels the particles. We further discover that the swimming direction is determined by the particle orientation. To enable navigation of the swimmers, we propose a new optomechanical approach to drive the in-plane rotation of Janus particles under a temperature-gradient-induced electrical field using a focused laser beam. Timing the rotation laser beam allows us to position the particles at any desired orientation and thus to actively control the swimming direction with high efficiency. By incorporating dark-field optical imaging and a feedback control algorithm, we achieve automated propelling and navigation of the microswimmers. Our opto-thermoelectric microswimmers could find applications in the study of opto-thermoelectrical coupling in dynamic colloidal systems, active matter, biomedical sensing, and targeted drug delivery.

A practical guide to active colloids: choosing synthetic model systems for soft matter physics research

Synthetic active colloids that harvest energy stored in the environment and swim autonomously are a popular model system for active matter. This emerging field of research sits at the intersection of materials chemistry, soft matter physics, and engineering, and thus cross-talk among researchers from different backgrounds becomes critical yet difficult. To facilitate this interdisciplinary communication, and to help soft matter physicists with choosing the best model system for their research, we here present a tutorial review article that describes, in appropriate detail, six experimental systems of active colloids commonly found in the physics literature. For each type, we introduce their background, material synthesis and operating mechanisms and notable studies from the soft matter community, and comment on their respective advantages and limitations. In addition, the main features of each type of active colloid are summarized into two useful tables. As materials chemists and engineers, we intend for this article to serve as a practical guide, so those who are not familiar with the experimental aspects of active colloids can make more informed decisions and maximize their creativity.

Frequency Response of Induced-Charge Electrophoretic Metallic Janus Particles

The ability to manipulate and control active microparticles is essential for designing microrobots for applications. This paper describes the use of electric and magnetic fields to control the direction and speed of induced-charge electrophoresis (ICEP) driven metallic Janus microrobots. A direct current (DC) magnetic field applied in the direction perpendicular to the electric field maintains the linear movement of particles in a 2D plane. Phoretic force spectroscopy (PFS), a phase-sensitive detection method to detect the motions of phoretic particles, is used to characterize the frequency-dependent phoretic mobility and drag coefficient of the phoretic force. When the electric field is scanned over a frequency range of 1 kHz-1 MHz, the Janus particles exhibit an ICEP direction reversal at a crossover frequency at ~30 kH., Below this crossover frequency, the particle moves in a direction towards the dielectric side of the particle, and above this frequency, the particle moves towards the metallic side. The ICEP phoretic drag coefficient measured by PFS is found to be similar to that of the Stokes drag. Further investigation is required to study microscopic interpretations of the frequency at which ICEP mobility switched signs and the reason why the magnitudes of the forward and reversed modes of ICEP are so different.

Optical Patterning of Two-Dimensional Materials

Recent advances in the field of two-dimensional (2D) materials have led to new electronic and photonic devices enabled by their unique properties at atomic thickness. Structuring 2D materials into desired patterns on substrates is often an essential and foremost step for the optimum performance of the functional devices. In this regard, optical patterning of 2D materials has received enormous interest due to its advantages of high-throughput, site-specific, and on-demand fabrication. Recent years have witnessed scientific reports of a variety of optical techniques applicable to patterning 2D materials. In this minireview, we present the state-of-the-art optical patterning of 2D materials, including laser thinning, doping, phase transition, oxidation, and ablation. Several applications based on optically patterned 2D materials will be discussed as well. With further developments, optical patterning is expected to hold the key in pushing the frontiers of manufacturing and applications of 2D materials.

Cargo capture and transport by colloidal swarms

Controlling active colloidal particle swarms could enable useful microscopic functions in emerging applications at the interface of nanotechnology and robotics. Here, we present a computational study of controlling self-propelled colloidal particle propulsion speeds to cooperatively capture and transport cargo particles, which otherwise produce random dispersions. By sensing swarm and cargo coordinates, each particle's speed is actuated according to a control policy based on multiagent assignment and path planning strategies that navigate stochastic particle trajectories to targets around cargo. Colloidal swarms are shown to dynamically cage cargo at their center via inward radial forces while simultaneously translating via directional forces. Speed, power, and efficiency of swarm tasks display emergent coupled dependences on swarm size and pair interactions and approach asymptotic limits indicating near-optimal performance. This scheme exploits unique interactions and stochastic dynamics in colloidal swarms to capture and transport microscopic cargo in a robust, stable, error-tolerant, and dynamic manner.

Quorum-sensing active particles with discontinuous motility

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields

There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO₂-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.

Active particles in noninertial frames: How to self-propel on a carousel

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Optimal Navigation of Self-Propelled Colloids

Controlling the navigation of self-propelled, Brownian colloids in complex microstructured environments ( e.g., porous media and tumor vasculature) is important to emerging applications ( e.g., enhanced oil recovery and drug delivery). Here, we report a feedback control strategy by which to navigate self-propelled colloids through free space and increasingly complex mazes. Colloid rod position and orientation within mazes is sensed in real time, and instantaneous propulsion along the rod long axis can be actuated via light intensity. However, because uncontrolled rod rotational diffusion determines the propulsion direction, feedback control based on a policy is required to decide how to actuate propulsion magnitude versus colloid position and orientation within mazes. By considering stochastic rod dynamics including self-propulsion, translational-rotational diffusion, and rod-maze interactions, a Markov decision process framework is used to determine optimal control policies to navigate between start and end points in minimal time. The free-space navigation optimal policy effectively reduces to a simple heuristic in which propulsion is actuated only when particles point toward the target. The emergent structure of optimal control policies in mazes is based on the practice of globally following the shortest geometric paths; however, locally, propulsion is actuated to either follow paths toward the target or to produce collisions with maze features as part of generating more-favorable positions and orientations. Findings show how the coupled effects of maze size, propulsion speed, control update time, and relative particle translational and rotational diffusivities influence navigation performance.

Clustering and phase separation of circle swimmers dispersed in a monolayer

We perform Brownian dynamics simulations in two dimensions to study the collective behavior of circle swimmers, which are driven by both, an (effective) translational and rotational self-propulsion, and interact via steric repulsion. We find that active rotation generally opposes motility-induced clustering and phase separation, as demonstrated by a narrowing of the coexistence region upon increase of the propulsion angular velocity. Moreover, although the particles are intrinsically assigned to rotate counterclockwise, a novel state of clockwise vortices emerges at an optimal value of the effective propulsion torque. We propose a simple gear-like model to capture the underlying mechanism of the clockwise vortices.

Autophoretic motion in three dimensions

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary conditions, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.

Active colloids with collective mobility status and research opportunities

The collective mobility of active matter (self-propelled objects that transduce energy into mechanical work to drive their motion, most commonly through fluids) constitutes a new frontier in science and achievable technology. This review surveys the current status of the research field, what kinds of new scientific problems can be tackled in the short term, and what long-term directions are envisioned. We focus on: (1) attempts to formulate design principles to tailor active particles; (2) attempts to design principles according to which active particles interact under circumstances where particle-particle interactions of traditional colloid science are augmented by a family of nonequilibrium effects discussed here; (3) attempts to design intended patterns of collective behavior and dynamic assembly; (4) speculative links to equilibrium thermodynamics. In each aspect, we assess achievements, limitations, and research opportunities.

Active colloids as mobile microelectrodes for unified label-free selective cargo transport

Utilization of active colloids to transport both biological and inorganic cargo has been widely examined in the context of applications ranging from targeted drug delivery to sample analysis. In general, carriers are customized to load one specific target via a mechanism distinct from that driving the transport. Here we unify these tasks and extend loading capabilities to include on-demand selection of multiple nano/micro-sized targets without the need for pre-labelling or surface functionalization. An externally applied electric field is singularly used to drive the active cargo carrier and transform it into a mobile floating electrode that can attract (trap) or repel specific targets from its surface by dielectrophoresis, enabling dynamic control of target selection, loading and rate of transport via the electric field parameters. In the future, dynamic selectivity could be combined with directed motion to develop building blocks for bottom-up fabrication in applications such as additive manufacturing and soft robotics.

Janus particles have a surface with two distinct physical or chemical properties; when one side is conducting and the other dielectric, the particles can be guided by an electric field. Here the authors polarize the metallic hemisphere of the particle which enables selective pickup and release of cargo.

Gas Bubbles Stabilized by Janus Particles with Varying Hydrophilic-Hydrophobic Surface Characteristics

Micrometer-sized polymer-grafted gold-silica (Au-SiO₂) Janus particles were fabricated by vacuum evaporation followed by polymer grafting. The Janus particle diameter, diameter distribution, morphology, surface chemistry, and water wettability were characterized by optical microscopy, scanning electron microscopy, X-ray photoelectron spectroscopy, and contact angle measurements. The optical microscopy results showed that the polystyrene (PS)-grafted Au-SiO₂ Janus particles exhibited monolayer adsorption at the air-water interface and could stabilize bubbles, preventing their coalescence for more than 1 month. The hydrophobic PS-grafted Au and hydrophilic SiO₂ surfaces were exposed to the air and water phases, respectively. Bare Au-SiO₂ and poly(2-(perfluorobutyl)ethyl methacrylate) (PPFBEM)-grafted Au-SiO₂ Janus particles could also stabilize bubbles for up to 2 weeks. By contrast, bare silica particles did not stabilize bubbles and were dispersed in water. The bubbles that formed in the PS-grafted Janus particle system were more stable than those formed in the bare Au-SiO₂ Janus particles, PPFBEM-grafted Au-SiO₂ Janus particles, and SiO₂ particle systems because of the high adsorption energy of the PS-grafted particles at the air-water interface.

Orientation Control of Hemispherical Janus Particles and Metal Coating on the Selective Surface To Excite Surface Plasmon Polaritons in the Micro-Kretschmann Geometry

Asymmetric-shaped particles (the Janus particle) are difficult to be arranged in a uniform orientation on a solid substrate. This difficulty prevents further modification of the selective surface of the particles for fabrication of the Janus particles with anisotropy of the shape and surface. We successfully arranged hemispherical particles in a uniform orientation at the air-water interface. The particles were arranged on the solid substrate in a uniform orientation by transferring the particle film onto the substrate. This arrangement enabled the fabrication of the Janus particles with anisotropy of the shape and surface by selective deposition of a film on either the equatorial plane or the spherical surface. Additionally, we demonstrated the function of the microscopic Kretschmann geometry for excitation of the surface plasmon polaritons of a thin metal film on the equatorial plane of a single hemispherical particle.