Diffusive behaviors of circle-swimming motors

Generic Rules for Distinguishing Autophoretic Colloidal Motors

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.

Memory effects in spiral diffusion of rotary self-propellers

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)10.1103/PhysRevE.94.030601] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Designing circle swimmers: Principles and strategies

Various microswimmers move along circles rather than straight lines due to their swimming mechanisms, body shapes, or hydrodynamic effects. In this paper, we adopt the concepts of stochastic thermodynamics to analyze circle swimmers confined to a two-dimensional plane and study the trade-off relations between various physical quantities, such as precision, energy cost, and rotational speed. Based on these findings, we predict principles and strategies for designing microswimmers of special optimized functions under limited energy resource conditions, which will bring new experimental inspiration for designing smart motors.

Active colloids orbiting giant vesicles

Living or artificial self-propelled colloidal particles show original dynamics when they interact with other objects like passive particles, interfaces or membranes. These active colloids can transport small cargos or can be guided by passive objects, performing simple tasks that could be implemented in more complex systems. Here, we present an experimental investigation at the single particle level of the interaction between isolated active colloids and giant unilamellar lipid vesicles. We observed a persistent orbital motion of the active particle around the vesicle, which is independent of both the particle and the vesicle sizes. Force and torque transfers between the active particle and the vesicle is also described. These results differ in many aspects from recent theoretical and experimental reports on active particles interacting with solid spheres or liquid drops, and may be relevant for the study of swimming particles interacting with cells in biology or with microplastics in environmental science.

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.

Two-dimensional active motion

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

Janus Colloids Actively Rotating on the Surface of Water

Biological or artificial microswimmers move performing trajectories of different kinds such as rectilinear, circular, or spiral ones. Here, we report on circular trajectories observed for active Janus colloids trapped at the air-water interface. Circular motion is due to asymmetric and nonuniform surface properties of the particles caused by fabrication. Motion persistence is enhanced by the partial wetted state of the Janus particles actively moving in two dimensions at the air-water interface. The slowing down of in-plane and out-of-plane rotational diffusions is described and discussed.

Intermediate scattering function of an anisotropic Brownian circle swimmer

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

Multiwavelength Light-Responsive Au/B-TiO2 Janus Micromotors

Conventional photocatalytic micromotors are limited to the use of specific wavelengths of light due to their narrow light absorption spectrum, which limits their effectiveness for applications in biomedicine and environmental remediation. We present a multiwavelength light-responsive Janus micromotor consisting of a black TiO₂ microsphere asymmetrically coated with a thin Au layer. The black TiO₂ microspheres exhibit absorption ranges between 300 and 800 nm. The Janus micromotors are propelled by light, both in H₂O₂ solutions and in pure H₂O over a broad range of wavelengths including UV, blue, cyan, green, and red light. An analysis of the particles' motion shows that the motor speed decreases with increasing wavelength, which has not been previously realized. A significant increase in motor speed is observed when exploiting the entire visible light spectrum (>400 nm), suggesting a potential use of solar energy, which contains a great portion of visible light. Finally, stop-go motion is also demonstrated by controlling the visible light illumination, a necessary feature for the steerability of micro- and nanomachines.

Diffusion of active chiral particles

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

Catalytic Locomotion of Core-Shell Nanowire Motors

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

Dynamic self-assembly of microscale rotors and swimmers

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

Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?

The self-propulsion of artificial and biological microswimmers (or active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e. that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand resistance matrix and formally external effective forces and torques. This is consistent with experimental findings on the circular motion of artificial asymmetric microswimmers driven by self-diffusiophoresis. The concept of effective self-propulsion forces and torques significantly facilitates the understanding of the swimming paths, e.g. for a microswimmer under gravity. However, this concept has its limitations when the self-propulsion mechanism of a swimmer is disturbed either by another particle in its close vicinity or by interactions with obstacles, such as a wall.

Spinning Janus doublets driven in uniform ac electric fields

We provide an experimental proof of concept for a robust, continuously rotating microstructure-consisting of two metallodielectric (gold-polystyrene) Janus particles rigidly attached to each other-which is driven in uniform ac fields by asymmetric induced-charge electro-osmosis. The pairs (doublets) are stabilized on the substrate surface which is parallel to the plane of view and normal to the direction of the applied electric field. We find that the radius of orbit and angular velocity of the pair are predominantly dependent on the relative orientations of the interfaces between the metallic and dielectric hemispheres and that the electrohydrodynamic particle-particle interactions are small. Additionally, we verify that both the angular and linear velocities of the pair are proportional to the square of the applied field which is consistent with the theory for nonlinear electrokinetics. A simple kinematic rigid body model is used to predict the paths and doublet velocities (angular and linear) based on their relative orientations with good agreement.

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.