Self-assembled autonomous runners and tumblers

De-Novo Design of Actively Spinning and Gyrating Spherical Micro-Vesicles

Self-propelled lipid-based artificial cells that can achieve controlled rotation and directed translation present significant potential for biomedical applications, yet their engineering poses considerable challenges. Lipid vesicles synthesized via solution-based methods naturally adopt isotropic spherical shapes. Active motion of these spherical objects requires symmetry breaking and rigidity. In this study, giant vesicles are employed as chassis, utilizing enzymes that undergo cyclic, non-reciprocal conformational changes as power sources. Weak, transient protein-protein interactions induce lipid ordering leading to rigidity and spontaneous symmetry breaking. Upon activation of enzyme reactions, these spherical vesicles demonstrate a variety of motion patterns, from pure spinning to 3D spiral trajectories. From experiments and simulations, it is demonstrated how such motion enables the vesicles to cross complex barriers. By utilizing biocompatible and scalable materials, The methodology establishes a solid framework for the design of such self-propelled systems. The work paves the way for advancements in biomedical and environmental technologies such as targeted drug delivery and active matter research.

Direct measurement of self-diffusiophoretic force generated by active colloids of different patch coverage using optical tweezers

HYPOTHESIS

Synthetic micro/nanomotors are gaining extensive attention for various biomedical applications (especially in drug delivery) due to their ability to mimic the motion of biological micro/nanoscale swimmers. The feasibility of these applications relies on tight control of propulsion speed, direction, and type of motion (translation, circular, etc.) along with the exerted self-propulsive force. We propose to exploit the variation of both self-propulsion speed and force of active colloids with different patch coverages (with and without supporting layer) for engineering diffusiophoretic micro/nanomotors.

EXPERIMENTS

The microswimmers were designed at various patch coverages (10°, 30°, and 90°) with (Ti/Pt) and without (Pt) an adhesion layer for the catalytic patch through glancing angle metal deposition (GLAD) technique. Mean-square displacement (MSD) analysis was performed to obtain the self-propulsion parameters like speed and angular speed. Using optical tweezers (OT), the self-propulsive force was measured from the force power spectral density.

FINDINGS

The findings of our experiments suggest the non-requirement of any adhesion layer preceding the catalyst deposition since the Pt 10° colloidal batch had the maximal self-propulsion speed (4.61±0.3μm/s) and force (345±57fN) for 5% w/v H2O2 fuel concentration. Moreover, the self-propulsion speed and force decreased with increasing patch size, contrary to theoretical estimates. Also, the self-propulsive force obtained from MSD is 2 to 4 times lower in magnitude than the OT based force values. We believe that the self-propelling motion of the micromotors is possibly hindered due to interactions with the surface of the quartz cuvette during the optical microscopic analysis. Further, the MSD is limited to the self-propulsive motion in two dimensions. On the other hand, OT based force measurement involve trapping the particles in the bulk of the solution entirely avoiding the particle-substrate interactions. Hence, OT based force measurements are better than the propulsion velocity based stokes drag force estimates. We believe that this study can lay the foundation in designing efficient micro/nanomotors for translational biomedical applications.

Dynamics and Collective Behavior of Chemically Propelled Janus Sphere Dimers in Complex Solvents

The propulsion mechanisms and collective dynamics of chemically powered Janus sphere dimers at the micro- and nanoscales, confined in a quasi-two-dimensional geometry, are investigated using a coarse-grained microscopic dynamical model. These active Janus dimers consist of two identical Janus spheres, featuring a catalytic cap on one hemisphere. The chemical reaction taking place on the catalytic surface generates asymmetric concentration gradients of product molecules around the Janus sphere, leading to the self-propulsion of the dimers. Depending on the dimer configuration, they exhibit various motion behaviors such as forward propulsion, rotation, and restricted stochastic motion. Due to chemotactic effects and self-diffusiophoretic forces, ensembles of dimers spontaneously form diverse structures, such as transient clusters, stable rotational ensembles, and antiparallel aligned doublets. This study demonstrates that the configurations of Janus sphere dimers significantly influence their self-propulsion and collective behaviors, providing crucial insights for the design and control of active micro- and nanoscale systems.

Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets

In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.

Emergent gauge symmetry in active Brownian matter

We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).

Symmetrical Catalytic Colloids Display Janus-Like Active Brownian Particle Motion

Catalytic Janus colloids, with one hemi-sphere covered by a hydrogen peroxide reduction catalyst such as platinum, represent one of the most experimentally explored examples of self-motile active colloid systems. This paper comparatively investigates the motile behavior of symmetrical catalytic colloids produced by a solution-based metal salt reduction process. Despite the significant differences in the distribution of catalytic activity, this study finds that the motion produced by symmetrical colloids is equivalent to that previously reported for Janus colloids. It also shows that introducing a Janus structure to the symmetrical colloids via masking does not significantly modify their motion. These findings could indicate that very subtle variations in surface reactivity can be sufficient to produce Janus-like active Brownian particle-type motion, or that a symmetry-breaking phenomena is present. The study will consequently motivate fresh theoretical attention and also demonstrate a straightforward route to access large quantities of motile active colloids, which are expected to show subtly different phenomenology compared to those with Janus structures.

Magnetically locked Janus particle clusters with orientation-dependent motion in AC electric fields

Active particles, or micromotors, locally dissipate energy to drive locomotion at small length scales. The type of trajectory is generally fixed and dictated by the geometry and composition of the particle, which can be challenging to tune using conventional fabrication procedures. Here, we report a simple, bottom-up method to magnetically assemble gold-coated polystyrene Janus particles into "locked" clusters that display diverse trajectories when stimulated by AC electric fields. The orientation of particles within each cluster gives rise to distinct modes of locomotion, including translational, rotational, trochoidal, helical, and orbital. We model this system using a simplified rigid beads model and demonstrate qualitative agreement between the predicted and experimentally observed cluster trajectories. Overall, this system provides a facile means to scalably create micromotors with a range of well-defined motions from discrete building blocks.

Effect of speed fluctuations on the collective dynamics of active disks

Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate β. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of β, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.

Biphasic Chemokinesis of Mammalian Sperm

The female reproductive tract (FRT) continuously modulates mammalian sperm motion by releasing various clues as sperm migrate toward the fertilization site. An existing gap in our understanding of sperm migration within the FRT is a quantitative picture of how sperm respond to and navigate the biochemical clues within the FRT. In this experimental study, we have found that in response to biochemical clues, mammalian sperm display two distinct chemokinetic behaviors which are dependent upon the rheological properties of the media: chiral, characterized by swimming in circles; and hyperactive, characterized by random reorientation events. We used minimal theoretical modeling, along with statistical characterization of the chiral and hyperactive trajectories, to show that the effective diffusivity of these motion phases decreases with increasing concentration of chemical stimulant. In the context of navigation this concentration dependent chemokinesis suggests that the chiral or hyperactive motion refines the sperm search area within different FRT functional regions. Further, the ability to switch between phases indicates that sperm may use various stochastic navigational strategies, such as run and tumble or intermittent search, within the fluctuating and spatially heterogeneous environment of the FRT.

Microdynamics of active particles in defect-rich colloidal crystals

HYPOTHESIS

Because they are self-propulsive, active colloidal particles can interact with their environment in ways that differ from passive, Brownian particles. Here, we explore how interactions in different microstructural regions may contribute to colloidal crystal annealing.

EXPERIMENTS

We investigate active particles propagating in a quasi-2D colloidal crystal monolayer produced by alternating current electric fields (active-to-passive particle ratio ∼ 1:720). The active particle is a platinum Janus sphere propelled by asymmetric decomposition of hydrogen peroxide. Crystals are characterized for changes in void properties. The mean-squared-displacement of Janus particles are measured to determine how active microdynamics depend on the local microstructure, which is comprised of void regions, void-adjacent regions (defined as within three particle diameters of a void), and interstitial regions.

FINDINGS

At active particle energy E_A = 2.55 k_BT, the average void size increases as much as three times and the average void anisotropy increases about 40% relative to the passive case. The average microdynamical enhancement, <δ(t)>, of Janus particles in the crystal relative to an equivalent passive Janus particle is reduced compared to that of a free, active particle (<δ(t) > is 1.88 ± 0.04 and 2.66 ± 0.08, respectively). The concentration of active particles is enriched in void and void-adjacent regions. Active particles exhibit the greatest change in dynamics relative to the passive control in void-adjacent regions (<δ(t)> = 2.58 ± 0.06). The results support the conjecture that active particle microdynamical enhancement in crystal lattices is affected by local defect structure.

Fitting an active Brownian particle's mean-squared displacement with improved parameter estimation

The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or "short-time" form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.

Odd viscosity-induced Hall-like transport of an active chiral fluid

Broken time-reversal and parity symmetries in active spinner fluids imply a nondissipative "odd viscosity," engendering phenomena unattainable in traditional passive or active fluids. Here we show that the odd viscosity itself can lead to a Hall-like transport when the active chiral fluid flows through a quenched matrix of obstacles, reminiscent of the anomalous Hall effect. The Hall-like velocity depends significantly on the spinner activity and longitudinal flow due to the interplay between odd viscosity and spinner-obstacle collisions. Our findings underscore the importance of odd viscosity in active chiral matter and elucidate its essential role in the anomalous Hall-like effect.

Active colloidal molecules in activity gradients

We consider a rigid assembly of two active Brownian particles, forming an active colloidal dimer, in a gradient of activity. We show analytically that depending on the relative orientation of the two particles the active dimer accumulates in regions of either high or low activity, corresponding to, respectively, chemotaxis and antichemotaxis. Certain active dimers show both chemotactic and antichemotactic behavior, depending on the strength of the activity. Our coarse-grained Fokker-Planck approach yields an effective potential, which we use to construct a nonequilibrium phase diagram that classifies the dimers according to their tactic behavior. Moreover, we show that for certain dimers a higher persistence of the motion is achieved similar to the effect of a steering wheel in macroscopic devices. This work could be useful for designing autonomous active colloidal structures which adjust their motion depending on the local activity gradients.

Diffusion of chiral active particles in a Poiseuille flow

We study the diffusive behavior of chiral active (self-propelled) Brownian particles in a two-dimensional microchannel with a Poiseuille flow. Using numerical simulations, we show that the behavior of the transport coefficients of particles, for example, the average velocity v and the effective diffusion coefficient D_{eff}, strongly depends on flow strength u_{0}, translational diffusion constant D_{0}, rotational diffusion rate D_{θ}, and chirality of the active particles Ω. It is demonstrated that the particles can exhibit upstream drift, resulting in a negative v, for the optimal parameter values of u_{0}, D_{θ}, and Ω. Interestingly, the direction of v can be controlled by tuning these parameters. We observe that for some optimal values of u_{0} and Ω, the chiral particles aggregate near a channel wall and the corresponding D_{eff} are enhanced. However, for the nonchiral particles (Ω=0), D_{eff} is suppressed by the presence of Poiseuille flow. It is expected that these findings have a great potential for developing microfluidic and lab-on-a-chip devices for separating the active particles.

Reconfigurable artificial microswimmers with internal feedback

Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters' motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.

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.

Statistics of pathogenic bacteria in the search of host cells

A crucial phase in the infection process, which remains poorly understood, is the localization of suitable host cells by bacteria. It is often assumed that chemotaxis plays a key role during this phase. Here, we report a quantitative study on how Salmonella Typhimurium search for T84 human colonic epithelial cells. Combining time-lapse microscopy and mathematical modeling, we show that bacteria can be described as chiral active particles with strong active speed fluctuations, which are of biological, as opposed to thermal, origin. We observe that there exists a giant range of inter-individual variability of the bacterial exploring capacity. Furthermore, we find Salmonella Typhimurium does not exhibit biased motion towards the cells and show that the search time statistics is consistent with a random search strategy. Our results indicate that in vitro localization of host cells, and also cell infection, are random processes, not involving chemotaxis, that strongly depend on bacterial motility parameters.

Ultrafast Directional Janus Pt-Mesoporous Silica Nanomotors for Smart Drug Delivery

Development of bioinspired nanomachines with an efficient propulsion and cargo-towing has attracted much attention in the last years due to their potential biosensing, diagnostics, and therapeutics applications. In this context, self-propelled synthetic nanomotors are promising carriers for intelligent and controlled release of therapeutic payloads. However, the implementation of this technology in real biomedical applications is still facing several challenges. Herein, we report the design, synthesis, and characterization of innovative multifunctional gated platinum-mesoporous silica nanomotors constituted of a propelling element (platinum nanodendrite face), a drug-loaded nanocontainer (mesoporous silica nanoparticle face), and a disulfide-containing oligo(ethylene glycol) chain (S-S-PEG) as a gating system. These Janus-type nanomotors present an ultrafast self-propelled motion due to the catalytic decomposition of low concentrations of hydrogen peroxide. Likewise, nanomotors exhibit a directional movement, which drives the engines toward biological targets, THP-1 cancer cells, as demonstrated using a microchip device that mimics penetration from capillary to postcapillary vessels. This fast and directional displacement facilitates the rapid cellular internalization and the on-demand specific release of a cytotoxic drug into the cytosol, due to the reduction of the disulfide bonds of the capping ensemble by intracellular glutathione levels. In the microchip device and in the absence of fuel, nanomotors are neither able to move directionally nor reach cancer cells and deliver their cargo, revealing that the fuel is required to get into inaccessible areas and to enhance nanoparticle internalization and drug release. Our proposed nanosystem shows many of the suitable characteristics for ideal biomedical destined nanomotors, such as rapid autonomous motion, versatility, and stimuli-responsive controlled drug release.

Active particles with polar alignment in ring-shaped confinement

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

The dynamics and self-assembly of chemically self-propelled sphere dimers

The dynamics of chemically powered sphere dimers at the micro- and nano-scales confined in a quasi-two-dimensional geometry are investigated. The dimer consists of a Janus particle and a non-catalytic sphere. A chemical reaction taking place on the catalytic surface of the Janus particle creates asymmetric concentration gradients that give rise to the self-propulsion of both rotation and translation of the dimer. Due to the chemical interactions, ensembles of dimers spontaneously form anti-parallel aligned doublets that exhibit the same rotation direction and lose translational motion. The chirality of the dimer plays an important role in the process of doublet formation. The study displays new collective dynamics and structures when both translational and rotational self-propulsion occur.

Hydrodynamic interactions in squirmer dumbbells: active stress-induced alignment and locomotion

Hydrodynamic interactions are fundamental for the dynamics of swimming self-propelled particles. Specifically, bonds between microswimmers enforce permanent spatial proximity and, thus, enhance emergent correlations by microswimmer-specific flow fields. We employ the squirmer model to study the swimming behavior of microswimmer dumbbells by mesoscale hydrodynamic simulations, where the squirmers' rotational motion is geometrically unrestricted. An important aspect of the applied particle-based simulation approach-the multiparticle collision dynamics method-is the intrinsic account for thermal fluctuations. We find a strong effect of active stress on the motility of dumbbells. In particular, pairs of strong pullers exhibit orders of magnitude smaller swimming efficiency than pairs of pushers. This is a consequence of the inherent thermal fluctuations in combination with the strong coupling of the squirmers' rotational motion, which implies non-exponentially decaying auto- and cross-correlation functions of the propulsion directions, and active stress-dependent characteristic decay times. As a consequence, specific stationary-state relative alignments of the squirmer propulsion directions emerge, where pullers are preferentially aligned in an antiparallel manner along the bond vector, whereas pushers are preferentially aligned normal to the bond vector with a relative angle of approximately 60° at weak active stress, and one of the propulsion directions is aligned with the bond at strong active stress. The distinct differences between dumbbells comprised of pusher or pullers suggest means to control microswimmer assemblies for future microbot applications.

Catalytically propelled 3D printed colloidal microswimmers

Synthetic microswimmers are widely employed model systems in the studies of out-of-equilibrium phenomena. Unlike biological microswimmers which naturally occur in various shapes and forms, synthetic microswimmers have so far been limited almost exclusively to spherical shapes. Here, we exploit 3D printing to produce microswimmers with complex shapes in the colloidal size regime. We establish the flexibility of 3D printing by two-photon polymerisation to produce particles smaller than 10 microns with a high-degree of shape complexity. We further demonstrate that 3D printing allows control over the location of the active site through orienting the particles in different directions during printing. We verify that particles behave colloidally by imaging their motion in the passive and active states and by investigating their mean square displacement. In addition, we find that particles exhibit shape-dependant behavior, thereby demonstrating the potential of our method to launch a wide-range of in-depth studies into shape-dependent active motion and behaviour.

Diffusion-Based Height Analysis Reveals Robust Microswimmer-Wall Separation

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit "ypsotaxis," a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity induced, posing restrictions on future modeling of their still-debated propulsion mechanism.

Active Assembly of Spheroidal Photocatalytic BiVO4 Microswimmers

We create single-component photocatalytic bismuth vanadate (BiVO₄) microswimmers with a spheroidal shape that move individually upon irradiation without any asymmetrization step. These particles form active assemblies which we investigate combining an experimental approach with numerical simulations and analytical calculations. We systematically explore the speed and assembly of the swimmers into clusters of up to four particles and find excellent agreement between experiment and theory, which helps us to understand motion patterns and speed trends. Moreover, different batches of particles can be functionalized separately, making them ideal candidates to fulfill a multitude of tasks, such as sensing or environmental remediation. To exemplify this, we coat our swimmers with silica (SiO₂) and selectively couple some of their modules to fluorophores in a way which does not inhibit self-propulsion. The present work establishes spheroidal BiVO₄ microswimmers as a versatile platform to design multifunctional microswimmers.

Waves in active matter: The transition from ballistic to diffusive behavior

We highlight the unique wavelike character observed in the relaxation dynamics of active systems via a Smoluchowski based theoretical framework and Brownian dynamic simulations. Persistent swimming motion results in wavelike dynamics until the advective swim displacements become sufficiently uncorrelated, at which point the motion becomes a random walk process characterized by a swim diffusivity, D^{swim}=U_{0}^{2}τ_{R}/[d(d-1)], dependent on the speed of swimming U_{0}, reorientation time τ_{R}, and reorientation dimension d. This change in behavior is described by a telegraph equation, which governs the transition from ballistic wavelike motion to long-time diffusive motion. We study the relaxation of active Brownian particles from an instantaneous source, and provide an explanation for the nonmonotonicity observed in the intermediate scattering function. Using our simple kinetic model we provide the density distribution for the diffusion of active particles released from a line source as a function of time, position, and the ratio of the activity to thermal energy. We extend our analysis to include the effects of an external field on particle spreading to further understand how reorientation events in the active force vector affect relaxation. The strength of the applied external field is shown to be inversely proportional to the decay of the wavelike structure. Our theoretical description for the evolution of the number density agrees with Brownian dynamic simulation data.

Pressure and diffusion of active matter with inertia

It has been discovered that active matter generates novel physical quantities such as the swim pressure. This quantity arises from the exchange of extra momentum between active particles and the boundaries of the system. Given its origin, this quantity can exist at different scales; hence microorganisms and larger organisms like fish or birds generate their own swim pressure. For larger organisms or for high swimming speeds, inertia cannot necessarily be neglected; hence in this paper, we start by calculating analytically the effect of finite translational and rotational particles' inertia on the diffusion of a system of noninteracting spherical active Brownian particles. From this analysis, an enhanced diffusion coefficient due to rotational inertia is obtained, and an alternative effective persistence length and an alternative reorientation time, both sensitive to rotational inertia, are also identified. Afterwards, and to see the implications of finite inertia on bulk properties, the pressure of this system is elucidated by calculating its respective swim and Reynolds pressures. It is found that their sum becomes asymptotically sensitive to the square root of its rotational inertia. To validate our analytical results, Langevin dynamics simulations are also performed showing an excellent agreement between our theoretical predictions and the numerical results.

Enhanced Propulsion of Urease-Powered Micromotors by Multilayered Assembly of Ureases on Janus Magnetic Microparticles

Enzyme-powered micro/nanomotors propelled by biocompatible fuels generally show a weak propulsive force, which greatly limits their applications in complex biological environments. Herein, we have developed a novel and versatile approach to significantly enhance the propulsion of enzyme-powered micromotors by multilayered assembly of enzymes. As an example, multilayers of biotinylated ureases (BU) were asymmetrically immobilized on biotinylated Janus Au/magnetic microparticles (MMPs) with the assistance of streptavidin (SA). When the mass ratio of BU into SA and the amount of BU used in the assembly process are increased, the amount of urease immobilized on the biotinylated Janus Au/MMPs increased monotonously while the migration speed of the micromotor was augmented gradually until a saturated value. The as-optimized micromotors can be self-propelled with an average speed up to about 21.5 ± 0.8 μm/s at physiological urea concentrations (10 mM), which is five times faster than that of the monolayered counterparts and two times faster than that of the previously reported values. Owing to the enhanced thrust, the micromotors can move in liquids with viscosities similar to that of blood. In addition, with the inherent magnetic property of MMPs, the micromotors can exhibit fast magnetic separation and controllable motion direction by external magnetic fields. Our results provide a new pathway for designing high-efficient enzyme-powered micro/nanomotors and thereby promote their biomedical applications.

Active rotational dynamics of a self-diffusiophoretic colloidal motor

The dynamics of a spherical chemically-powered synthetic colloidal motor that operates by a self-diffusiophoretic mechanism and has a catalytic domain of arbitrary shape is studied using both continuum theory and particle-based simulations. The motor executes active rotational motion when self-generated concentration gradients and interactions between the chemical species and colloidal motor surface break spherical symmetry. Local variations of chemical reaction rates on the motor catalytic surface with catalytic domain sizes and shapes provide such broken symmetry conditions. A continuum theoretical description of the active rotational motion is given, along with the results of particle-based simulations of the active dynamics. From these results a detailed description of the factors responsible for the active rotational dynamics can be given. Since active rotational motion often plays a significant part in the nature of the collective dynamics of many-motor systems and can be used to control motor motion in targeted cargo transport, our results should find applications beyond those considered here.

Dynamics of a ratchet gear powered by an active granular bath

Recent experiments show universal features of ratchet gear dynamics that are powered by different types of active baths. We investigate further for the case of a ratchet gear in a bath of self-propelling granular rods (SPRs). The resulting angular velocity was found to follow a nonmonotonic dependence to the SPR concentration similar to the observation from other active bath systems. This behavior is caused by the interplay of the momentum transfer of the SPRs in the trapping regions of the gear and the mean velocity of the SPRs inside the bath. For all SPR concentrations, we found that the angular velocity is proportional to the product of the number of SPRs pushing the gear and the SPRs mean velocity.

Slip Length Dependent Propulsion Speed of Catalytic Colloidal Swimmers near Walls

Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. Here, we report experimental measurements of a significant dependence of such microswimmers' speed on the nearby substrate material. We find that speeds scale with the solution contact angle θ on the substrate, which relates to the associated hydrodynamic substrate slip length, as V∝(cosθ+1)^{-3/2}. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynamic slip at nearby walls, though often unconsidered, can significantly impact microswimmer self-propulsion.

Tuning the Random Walk of Active Colloids: From Individual Run-and-Tumble to Dynamic Clustering

Active particles such as swimming bacteria or self-propelled colloids spontaneously self-organize into large-scale dynamic structures. The emergence of these collective states from the motility pattern of the individual particles, typically a random walk, is yet to be probed in a well-defined synthetic system. Here, we report the experimental realization of tunable colloidal motion that reproduces run-and-tumble and Lévy trajectories. We utilize the Quincke effect to achieve controlled sequences of repeated particle runs and random reorientations. We find that a population of these random walkers exhibit behaviors reminiscent of bacterial suspensions such as dynamic clusters and mesoscale turbulentlike flows.

Mesoscopic simulations of anisotropic chemically powered nanomotors

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Dynamics near planar walls for various model self-phoretic particles

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

Transition from Linear to Circular Motion in Active Spherical-Cap Colloids

Nonspherical self-propelling colloidal particles offer many possibilities for creating a variety of active motions. In this work, we report on the transition from linear to circular motion of active spherical-cap particles near a substrate. Self-propulsion is induced by self-diffusiophoresis by catalytic decomposition of hydrogen peroxide (H₂O₂) on one side of the particle. Asymmetric distribution of reaction products combined with the asymmetric shape of the particle gives rise to two types of motions depending upon the relative orientation of the particle with respect to the underlying substrate. At a low concentration of H₂O₂, linear active motion is observed, whereas increasing the H₂O₂ concentration leads to persistent circular motion. However, the speed of self-propulsion is nearly independent of the size of the particle. The study demonstrates the use of nonspherical particles to create linear and circular motion by varying the fuel concentration.

Disintegrating polymer multilayers to jump-start colloidal micromotors

Colloidal systems with autonomous mobility are attractive alternatives to static particles for diverse applications. We present a complementary approach using pH-triggered disintegrating polymer multilayers for self-propulsion of swimmers. It is illustrated both experimentally and theoretically that homogenously coated swimmers exhibit higher velocity in comparison to their Janus-shaped counterparts. These swimmers show directional and random motion in microfluidic channels with a steep and shallow pH gradient, respectively. Further, a higher number of deposited polymer multilayers, steeper pH gradients and lower mass of the swimmers result in higher self-propulsion velocities. This new self-propulsion mechanism opens up unique opportunities to design, for instance, fast and yet biocompatible swimmers using the diverse tools of polymer chemistry to custom-synthesise the polymeric building blocks to assemble multilayers.

Visible Light Actuated Efficient Exclusion Between Plasmonic Ag/AgCl Micromotors and Passive Beads

Insight is provided into the collective behavior of visible-light photochemically driven plasmonic Ag/AgCl Janus particles surrounded by passive polystyrene (PS) beads. The active diffusion of single Janus particles and their clusters (small: consisting of two or three Janus particles and large: consisting of more than ten Janus particles), and their interaction with passive PS beads, are analyzed experimentally and in simulations. The diffusivity of active Janus particles, and thus the exclusive effect to passive PS beads, can be regulated by the number of single Janus particles in the cluster. On the simulation side, the Langevin equations of motion for self-propelled Janus particles and diffusing passive PS beads are numerically solved using Molecular-Dynamics simulations. The complex interactions of both subsystems, including elastic core-to-core interactions, short-range attraction, and effective repulsion due to light-induced chemical reactions are considered. This complex mixed system not only provides insight to the interactive effect between active visible light-driven self-propelled micromotors and passive beads, but also offers promise for implications in light-controlled propulsion transport and chemical sensing.

Self-Propulsion and Active Motion of Janus Ellipsoids

The propulsion of platinum-coated polystyrene prolate ellipsoids, as generated by catalytic decomposition of hydrogen peroxide, is characterized by direct visualization of the trajectories of the active particles. These Janus ellipsoids were fabricated by stretching micron-sized polystyrene spheres into different aspect ratios; half of the particle is then capped lengthwise along the ellipsoid's major axis, with platinum deposition. These particles exhibit complex dynamical trajectories in aqueous solutions of hydrogen peroxide of concentration in the range of 2-8% (w/v). In this range, a transition from three-dimensional passive Brownian motion to two-dimensional active motion is observed as the hydrogen peroxide concentration is increased. This transition from passive to active motion is complete by 4% (w/v) hydrogen peroxide. We quantify the effect of particle aspect ratio on the mean-squared displacement and mean-squared angular displacement at the highest hydrogen peroxide concentration. The two-dimensional trajectories of the individual particles were grouped into three categories for dynamical analysis. In the first category, ballistic ellipsoids translate at least 5 times more than purely diffusive ellipsoids at the characteristic time scale of rotational diffusion. In the second category, spinning ellipsoids move only short distances with a dominant rotation about the minor axis; this rotation persists for many revolutions. A third category captures trajectories that include both significant translation and rotation. We consider the physical origins of the observed categories of motion and extract the forces and torques generated by the catalytically generated propulsion as a function of aspect ratio. The particle velocity, and therefore the active force, increases with the aspect ratio.

Catalytic Janus Colloids: Controlling Trajectories of Chemical Microswimmers

Catalytic Janus colloids produce rapid motion in fluids by decomposing dissolved fuel. There is great potential to exploit these "autonomous chemical swimmers" in applications currently performed by diffusion limited passive colloids. Key application areas for colloids include transporting active ingredients for drug delivery, gathering analytes for medical diagnostics, and self-assembling into regular structures used for photonic materials and lithographic templating. For drug delivery and medical diagnostics, controlling colloidal motion is key in order to target therapies, and transport analytes through lab-on-a-chip devices. Here, the autonomous motion of catalytic Janus colloids can remove the current requirements to induce and control colloid motion using external fields, thereby reducing the technological complexity required for medical therapies and diagnostics. For materials applications exploiting colloidal self-assembly, the additional interactions introduced by catalytic activity and rapid motion are predicted to allow access to new reconfigurable and responsive structures. In order to realize these goals, it is vital to develop methods to control both individual colloidal paths and collective behavior in motile catalytic colloidal systems. However, catalytic Janus colloids' trajectories are randomized by Brownian effects, and so require new strategies in order to be harnessed for transport. This is achievable using a variety of different approaches. For example, self-assembly and control of catalyst geometry can introduce controlled amounts of rotary motion, or "spin" into chemical swimmer trajectories. Furthermore, rotary motion combined with gravity, produces well-defined orientated helical trajectories. In addition, when catalytic colloids interact with topographical features, such as edges and trenches, they are steered. This gives rise to a new approach for autonomous colloidal microfluidic transport that could be deployed in future lab-on-a-chip devices. Chemical gradients can also influence the motion of catalytic Janus colloids, for example, to cause collective accumulations at specific locations. However, at present, the predicted theoretical degree of control over this phenomenon has not been fully verified in experimental systems. Collective behavior control for chemical swimmers is also possible by exploiting the potential for the complex interactions in these systems to allow access to self-assembled, dynamic and reconfigurable ordered structures. Again, current experiments have not yet accessed the breadth of possible behavior. Consequently, continued efforts are required to understand and control these interaction mechanisms in real world systems. Ultimately, this will help realize the use of catalytic Janus colloids for tasks that require well-controlled motion and structural organization, enabling functions such as analyte capture and concentration, or targeted drug delivery.

A Supramolecular Approach to Nanoscale Motion: Polymersome-Based Self-Propelled Nanomotors

Autonomous micro- and nanoscale systems have revolutionized the way scientists look into the future, opening up new frontiers to approach and solve problems via a more bioinspired route. However, to achieve systems with higher complexity, superior output control, and multifunctionality, an in-depth study of the different factors that affect micro- and nanomotor behavior is crucial. From a fundamental perspective, the mechanical response of micro- and nanomotors still requires further study in order to have a better understanding of how exactly these systems operate and the different mechanisms of motion that can be combined into one system to achieve an optimal response. From a design engineering point of view, compatibility, degradability, specificity, sensitivity, responsiveness, and efficiency of the active systems fabricated to this point have to be addressed, with respect to the potential of these devices for biomedical applications. Nonetheless, optimizing the system with regards to all these areas is a challenging task with the micro- and nanomotors studied to date, as most of them consist of materials or designs that are unfavorable for further chemical or physical manipulation. As this new field of self-powered systems moves forward, the need for motor prototypes with different sizes, shapes, chemical functionalities, and architectures becomes increasingly important and will define not only the way active systems are powered, but also the methods for motor fabrication. Bottom-up supramolecular approaches have recently emerged as great candidates for the development of active structures that allow for chemical or physical functionalization, shape transformation, and compartmentalization, in a structure that provides a soft interface to improve molecular recognition and cell uptake. Our group pioneers the use of supramolecular structures as catalytically propelled systems via the fabrication of stomatocyte or tubular-shaped motors capable of displaying active motion in a substrate concentration-dependent fashion. This behavior demonstrates the potential of bottom-up assemblies for powering motion at the micro- or nanoscale, with a system that can be readily tuned and controlled at the molecular level. In this Account, we highlight the steps we have taken in order to understand and optimize the design of catalytically powered polymersome-based motors. Our research has been focused on addressing the importance of motor architecture, motion activation, direction control, and biological integration. While our work supports the feasibility of supramolecular structures for the design of active systems, we strongly believe that we are still in the initial stages of unveiling the full potential of supramolecular chemistry in the micro- and nanomotor field. We look forward to using this approach for the development of multifunctional and stimuli-responsive systems in the near future.

Examination of the Statistical Effects Associated with Tracking Propulsive Particles

Particle tracking of active colloidal particles can be used to compute mean-squared displacements that are fit to extract properties of the particles including the propulsive speed. Statistical errors in the mean-squared displacement leads to errors in the extracted properties especially for more weakly propelling particles. Brownian dynamics simulations in which the particle parameters are prescribed were used to examine the statistics of tracking self-propelling objects. It was found that the manner in which tracking data is analyzed has a profound impact on the precision and accuracy of measurements. To properly extract particle parameters, it was necessary to apply a nonlinear fit of the mean-squared displacement over a time region that includes transition behavior from ballistic to diffusive. The dependence of the statistics on the number of particles tracked and the length of movies was examined, showing how and why weakly propelling particles are difficult to analyze.

Probing the Spatiotemporal Dynamics of Catalytic Janus Particles with Single-Particle Tracking and Differential Dynamic Microscopy

We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations resolve the crossover between directed motion to orientational relaxation and allow us to discriminate active Brownian motion from other reorientation processes, e.g., run-and-tumble motion. A direct comparison to theoretical predictions reliably yields the rotational and translational diffusion coefficients of the particles, the mean and width of their speed distribution, and the temporal evolution of these parameters.

Active fluids at circular boundaries: swim pressure and anomalous droplet ripening

We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used to model a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles in their spatial distribution, chirality-induced currents, and the swim pressure they exert on the bounding surfaces. The results will then be used to predict the mechanical equilibria of suspended fluid enclosures (generically referred to as 'droplets') in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets. We show that, while droplets containing active particles behave in accordance with standard capillary paradigms when suspended in a normal bulk, those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk. In the latter case, the excess swim pressure results in non-monotonic dependence of the inside droplet pressure on the droplet radius; hence, revealing an anomalous regime of behavior beyond a threshold radius, in which the inside droplet pressure increases upon increasing the droplet size. Furthermore, for two interconnected droplets, mechanical equilibrium can occur also when the droplets have different sizes. We thus identify a regime of anomalous droplet ripening, where two unequal-sized droplets can reach a final state of equal size upon interconnection, in stark contrast with the standard Ostwald ripening phenomenon, implying shrinkage of the smaller droplet in favor of the larger one.

Re-entrant bimodality in spheroidal chiral swimmers in shear flow

We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.

Self-motile swimmers: Ultrasound driven spherical model

The concept of ultrasound acoustic driven self-motile swimmers which is the source of autonomous propulsion is the acoustic field generated by the swimmer due to the partial oscillation of its surface is investigated. Limiting the subject to a body with simple spherical geometry, it is analytically shown that the generated acoustic radiation force due to induction by asymmetric acoustic field in host medium is non-zero, which propels the device. Assuming low Reynolds number condition, the frequency-dependent swimming velocity is calculated as a function of design parameters and optimum operating condition is obtained. The proposed methodology will open a new path towards the micro- or molecular-sized self propulsive machines or mechanism with great applications in engineering, medicine and biology.

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.

Self-driven particles in linear flows and trapped in a harmonic potential

We present analytical expressions for the mean-square displacement of self-driven particles in general linear flows and trapped in a harmonic potential. The general expressions are applied to three types of linear flows, namely, shear flow, solid-body rotation flow, and extensional flow. By using Brownian dynamics simulations, the effect of trapping and external linear flows on the particles' distribution is also elucidated. These simulations also enabled us to validate our theoretical results.

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.

Rational design and dynamics of self-propelled colloidal bead chains: from rotators to flagella

The quest for designing new self-propelled colloids is fuelled by the demand for simple experimental models to study the collective behaviour of their more complex natural counterparts. Most synthetic self-propelled particles move by converting the input energy into translational motion. In this work we address the question if simple self-propelled spheres can assemble into more complex structures that exhibit rotational motion, possibly coupled with translational motion as in flagella. We exploit a combination of induced dipolar interactions and a bonding step to create permanent linear bead chains, composed of self-propelled Janus spheres, with a well-controlled internal structure. Next, we study how flexibility between individual swimmers in a chain can affect its swimming behaviour. Permanent rigid chains showed only active rotational or spinning motion, whereas longer semi-flexible chains showed both translational and rotational motion resembling flagella like-motion, in the presence of the fuel. Moreover, we are able to reproduce our experimental results using numerical calculations with a minimal model, which includes full hydrodynamic interactions with the fluid. Our method is general and opens a new way to design novel self-propelled colloids with complex swimming behaviours, using different complex starting building blocks in combination with the flexibility between them.