Motion of active particles, such as catalytic micro- and nano-motors, is usually characterized via either dynamic light scattering or optical microscopy. In both cases, speed of particles is obtained from the calculus of the mean square displacement (MSD) and typically, the theoretical formula of the MSD is derived from the motion equations of an active Brownian particle. One of the most commonly reported parameters is the speed of the particle, usually attributed to its propulsion, and is widely used to compare the motion efficiency of catalytic motors. However, it is common to find different methods to compute this parameter, which are not equivalent approximations and do not possess the same physical meaning. Here, we review the standard methods of speed analysis and focus on the errors that arise when analyzing the MSD of self-propelled particles. We analyze the errors from the computation of the instantaneous speed, as well as the propulsive speed and diffusion coefficient through fittings to parabolic equations, and we propose a revised formula for the motion analysis of catalytic particles moving with constant speed that can improve the accuracy and the amount of information obtained from the MSD. Moreover, we emphasize the importance of spotting the presence of different motion dynamics, such as particles with active angular speed or that move under the presence of drift, and how the breaking of ergodicity can completely change the analysis by considering particles with an exponentially decaying speed. In all cases, real data from enzymatically propelled micro-motors and simulations are used to back up the theories. Finally, we propose several analytical approaches and analyze limiting cases that will help to deal with these scenarios while still obtaining accurate results.
Self-propelled chemically powered synthetic micron and nano-scale motors are being intensively studied because of the wide range of potential applications that exploit their directed motion. This paper considers even smaller Ångström-size synthetic motors. Such very small motors in bulk solution display effects arising from their self-propulsion. Recent experiments have shown that small-molecule catalysts and single enzyme molecules exhibit properties that have been attributed to their chemical activity. Molecular dynamics is used to investigate the properties of very small Ångström-size synth…
In this Account, we describe how synthetic motors that operate by self-diffusiophoresis make use of a self-generated concentration gradient to drive motor motion. A description of propulsion by self-diffusiophoresis is presented for Janus particle motors comprising catalytic and noncatalytic faces. The properties of the dynamics of chemically powered motors are illustrated by presenting the results of particle-based simulations of sphere-dimer motors constructed from linked catalytic and noncatalytic spheres. The geometries of both Janus and sphere-dimer motors with asymmetric catalytic activi…
The single-particle and collective dynamics of systems comprising Janus motors, solvent and reactive solute species maintained in nonequilibrium states are investigated. Reversible catalytic reactions with the solute species take place on the catalytic faces of the motors, and the nonequilibrium states are established by imposing either constant-concentration reservoirs that feed and remove reactive species, or through out-of-equilibrium fluid phase reactions. We consider general intermolecular interactions between the Janus motor hemispheres and the reactive species. For single motors, we sho…
Starting from a microscopic model for a spherically symmetric active Janus particle, we study the interactions between two such active motors. The ambient fluid mediates a long range hydrodynamic interaction between two motors. This interaction has both direct and indirect hydrodynamic contributions. The direct contribution is due to the propagation of fluid flow that originated from a moving motor and affects the motion of the other motor. The indirect contribution emerges from the re-distribution of the ionic concentrations in the presence of both motors. Electric force exerted on the fluid …
Self-propulsion of a Janus droplet in a solution of surfactant, which reacts on a half of a drop surface, is studied theoretically. The droplet acts as a catalytic motor creating a concentration gradient, which generates its surface-tension-driven motion; the self-propulsion speed is rather high, $60\; {\rm μm/s}$ and more. This catalytic motor has several advantages over other micromotors: simple manufacturing, easily attained neutral buoyancy. In contrast to a single-fluid droplet, which demonstrates a self-propulsion as a result of symmetry breaking instability, for Janus one no stability t…
The collective behavior of chemically propelled sphere-dimer motors made from linked catalytic and noncatalytic spheres in a quasi-two-dimensional confined geometry is studied using a coarse-grained microscopic dynamical model. Chemical reactions at the catalytic spheres that convert fuel to product generate forces that couple to solvent degrees of freedom as a consequence of momentum conservation in the microscopic dynamics. The collective behavior of the many-body system is influenced by direct intermolecular interactions among the motors, chemotactic effects due to chemical gradients, hydro…
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 theo…
We demonstrate a catalytic control method for speeding up the single-molecule DNA motor introduced by Li and Tan [Nano Lett. {\bf 2}, 315 (2002)]. A key rate-limiting barrier in the reaction part of the cycle is the tendency for the second fuel strand $B$ to fold into the chair-like configuration of the original motor strand $M$. This seriously impedes the restoration reaction. We have designed a catalytic strand to inhibit the folding of $B$. Introduction of the catalyst speeds up the restoration reaction by roughly a factor of 2. The catalyst shows robust behavior for more than one cycle. Th…
Micro/Nano motors are micro to nano-sized particles and systems that are capable of motion in fluidic systems. Their motion can be a result of many mechanisms, one of the most well-known of which is electrolyte diffusiophoresis, in which asymmetric production of charged ions across the surface of the particle leads to phoresis. The focus of this work is to construct Urease motors with careful control of their Janus balance, i.e., to control the percentage of surface covered with the enzyme and study the effect of this asymmetry on the propulsion velocity of the particles. In that regard, we we…
Active media, whose constituents are able to move autonomously, display novel features that differ from those of equilibrium systems. In addition to naturally-occurring active systems such as populations of swimming bacteria, active systems of synthetic self-propelled nanomotors have been developed. These synthetic systems are interesting because of their potential applications in a variety of fields. Janus particles, synthetic motors of spherical geometry with one hemisphere that catalyzes the conversion of fuel to product and one noncatalytic hemisphere, can propel themselves in solution by …
Janus motors with chemically active and inactive hemispheres can operate only under nonequilibrium conditions where detailed balance is broken by fluxes of chemical species that establish a nonequilibrium state. A microscopic model for reversible reactive collisions on a Janus motor surface is constructed and shown to satisfy detailed balance. The model is used to study Janus particle reactive dynamics in systems at equilibrium where generalized chemical rate laws that include time-dependent rate coefficients with power-law behavior are shown to describe reaction rates. While maintaining rever…
Very small synthetic motors that make use of chemical reactions to propel themselves in solution hold promise for new applications in the development of new materials, science and medicine. The prospect of such potential applications, along with the fact that systems with many motors or active elements display interesting cooperative phenomena of fundamental interest, has made the study of synthetic motors an active research area. Janus motors, comprising catalytic and noncatalytic hemispheres, figure prominently in experimental and theoretical studies of these systems. While continuum models …
Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here, we use a series of simple models to analytically elucidate the propulsive effects of a solid boundary on passively actua…
Several designs for micro-devices for chemotaxis based on nano-motors are proposed. The nano- or micro-motors are the conventional Janus rods or spheres that are powered by the catalytic reaction of fuels such as hydrogen peroxide. It is shown how these can be linked to make a device that can follow a concentration gradient of the fuel. The feasibility of assembling the devices using micromanipulation or metallic deposition is discussed. A possible design principle is suggested for a device that follows the concentration gradient of an analyte other than the fuel.
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects, solute redistribution, and rotational diffusion are identified and shown to lead to a plethora of different regimes involving inertial, propulsive, anomalous, and diffusive behaviors. For symmetric active colloids, a regime is found where the mean-squared displacement has a super-diffusive $t^{3/2}$ behavior. At the longest time scales, an effective diffusion…
Micromotor and nanomotor particles are typically made using dense solid particles that can sediment or be trapped in confined flow environments. Creation of much larger motors should be possible if a very low-density system is used with sufficient strength to carry liquid and still experience propulsive motion. Light, dense millimotors should also be able to deform more than dense solid ones in constrictions. Millimotors are created from permeable capsules of bacterial cellulose that are coated with catalase-containing metal-organic frameworks, enabling reactive propulsion in aqueous hydrogen …
Dynamics of active or self-propulsive Brownian particles in nonequilibrium status, has recently attracted great interest in many fields including biological entities and artificial micro/nanoscopic motors6. Understanding of their dynamics can provide insight into the statistical properties of biological and physical systems far from equilibrium. Generally, active Brownian particles can involve either translational or rotational motion. Here, we report the translational dynamics of photon-activated gold nanoparticles (NPs) in liquid cell imaged by four-dimensional electron microscopy (4D-EM). U…
The fabrication of synthetic self-propelled particles and the experimental investigations of their dynamics have stimulated interest in self-generated phoretic effects that propel nano- and micron-scale objects. Theoretical modeling of these phenomena is often based on a continuum description of the solvent for different phoretic propulsion mechanisms, including, self-electrophoresis, self-diffusiophoresis and self-thermophoresis. The work in this paper considers various types of catalytic chemical reaction at the motor surface and in the bulk fluid that come into play in mesoscopic descriptio…
Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger than the corresponding values when chemical activity is absent. Various mechanisms have been proposed for such behavior, including, among others, force dipole interactions of molecular motors moving on filaments and collective hydrodynamic effects arising from active proteins. Simulations of a multi-component system containing active dumbbell molecules that cyc…
We study the velocity distribution of unicellular swimming algae Euglena gracilis using optical microscopy and theory. To characterize a peculiar feature of the experimentally observed distribution at small velocities we use the concept of active fluctuations, which was recently proposed for the description of stochastically self-propelled particles [Romanczuk, P. and Schimansky-Geier, L., Phys. Rev. Lett. 106, 230601 (2011)]. In this concept, the fluctuating forces arise due to internal random performance of the propulsive motor. The fluctuating forces are directed in parallel to the heading …
Here we demonstrate a synthetic micro-engine, based on long-range controlled movement of colloidal particles, which is induced by a local catalytic reaction. The directed motion at long timescales was achieved by placing specially designed magnetic capped colloids in a hydrogen peroxide solution at weak magnetic fields. The control of the motion of the particles was provided by changes of the concentration of the solution and by varying the strength of the applied magnetic field. Such synthetic objects can then be used not only to understand the fundamental driving processes but also be employ…
Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 $μ$m), Brownian thermal fluctuation forces are necessarily impor…
