Highly Efficient Active Colloids Driven by Galvanic Exchange Reactions

Micromotors are propelled by a variety of chemical reactions, with most of them being of catalytic nature. There are, however, systems based on redox reactions, which show clear benefits for efficiency. Here, we broaden the spectrum of suitable reactions to galvanic exchange processes, or an electrochemical replacement of a solid metal layer with dissolved ionic species of a more noble metal. We study the details of motility and the influence of different reaction parameters to conclude that these galvanophoretic processes circumvent several steps that lose efficiency in catalytic micromotors. Furthermore, we investigate the chemical process, the charge, and flow conditions that lead to this highly efficient new type of active motility. Toward a better understanding of the underlying processes, we propose an electrokinetic model that we numerically solve via finite elements.

Pt-SiO2 Janus Particles and the Water/Oil Interface: A Competition between Motility and Thermodynamics

Various aspects of the behavior of Janus particles near liquid/liquid interfaces have been studied through different experimental and theoretical realizations, but the effect of motility on the behavior of Janus particles near liquid/liquid interfaces has not been investigated, yet. Here, we demonstrate the ability to engineer the behavior of highly interfacial active Janus particles near a water/oil interface by introducing motility to the system. Passive, i.e., nonmotile, platinum-capped 8 μm silica (Pt-SiO₂) Janus particles exhibit a strong tendency to attach to water/oil interfaces with the Pt-cap facing the oil and the SiO₂ side facing the water phase. In contrast, we show that active, i.e., motile, 8 μm Pt-SiO₂ Janus particles approach the interface, orient in a sideways fashion with the Janus boundary perpendicular to the interface, and then swim in the vicinity of the interface similar to observations reported near solid/liquid interfaces. Active Pt-SiO₂ Janus particles near the water/oil interface show motility as a result of adding H₂O₂ to the particle solution. The decomposition of H₂O₂ into O₂ and H₂O creates a nonuniform gradient of O₂ around the particle that hydrodynamically interacts with the water/decalin boundary. The interaction enables rotation of the particle within the swimming plane that is parallel to the interface but restricts rotation in and out of the swimming plane, thereby preventing adsorption to the liquid/liquid interface.

Chemically Active Particles: From One to Few on the Way to Many

Chemically active particles suspended in a liquid solution can achieve self-motility by locally changing the chemical composition of the solution via catalytic reactions at their surfaces. They operate intrinsically out of equilibrium, continuously extracting free energy from the environment to power the dissipative self-motility. The effective interactions involving active particles are, in general, nonreciprocal and anisotropic, even if the particles have simple shapes (e.g., Janus spheres). Accordingly, for chemically active particles a very rich behavior of collective motion and self-assembly may be expected to emerge, including phenomena such as microphase separation in the form of kinetically stable, finite-sized aggregates. Here, I succinctly review a number of recent experimental studies that demonstrate the self-assembly of structures, involving chemically active Janus particles, which exhibit various patterns of motion. These examples illustrate concepts such as "motors made out of motors" (as suggestively named by Fischer [Fischer, P. Nat. Phys. 2018, 14, 1072]). The dynamics of assembly and structure formation observed in these systems can provide benchmark, in-depth testing of the current understanding of motion and effective interactions produced by chemical activity. Finally, one notes that these significant achievements are likely just the beginning of the field. Recently reported particles endowed with time-dependent chemical activity or switchable reaction mechanisms open the way for exciting developments, such as periodic reshaping of self-assembled structures based on man-made internal clocks.

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.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Thermodynamic approach to the self-diffusiophoresis of colloidal Janus particles

Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here, we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit self-propulsion in a demixing binary solvent. At variance with a slip velocity, we find that propulsion is due to forces at the poles that are perpendicular to the particle surface. Second, for catalytic swimmers driven through liberating chemical free energy we recover previous expressions. In both cases we argue that propulsion is due to asymmetric dissipation and not simply due to an asymmetric concentration of molecular solutes.

Experimental Study of the Motion of Patchy Particle Swimmers Near a Wall

In this work, we demonstrate our ability to precisely tailor the surface activity of self-propelled active colloids by varying the size of the active area. The quasi two-dimensional autonomous motion of spherical patchy particle swimmers is studied in a chemical environment in the vicinity of a solid boundary. Oxidative decomposition of hydrogen peroxide into oxygen and water occurs only on a well-defined Pt-coated section of the polystyrene particle surface. The asymmetric distribution of product molecules interacting with the particle leads to the autonomous motion, which is characterized as the patch size varies from 11 to 25 to 50% of the particle surface area. The phoretic motion of patchy particle swimmers is analytically predicted by a model developed by Popescu et al. and shows good agreement with the experimentally observed velocities when the influence of the wall on the preferential rotational motion of the particles near the solid boundary is considered. The study illustrates the potential to precisely engineer the motion of particles by controlling their properties rather than depending on changes in the environment.

Effective Interactions between Chemically Active Colloids and Interfaces

Chemically active colloids can achieve force- and torque-free motility ("self-propulsion") via the promotion, on their surface, of catalytic chemical reactions involving the surrounding solution. Such systems are valuable both from a theoretical perspective, serving as paradigms for nonequilibrium processes, as well as from an application viewpoint, according to which active colloids are envisioned to play the role of carriers ("engines") in novel lab-on-a-chip devices. The motion of such colloids is intrinsically connected with a "chemical field", i.e., the distribution near the colloid of the number densities of the various chemical species present in the solution, and with the hydrodynamic flow of the solution around the particle. In most of the envisioned applications, and in virtually all reported experimental studies, the active colloids operate under spatial confinement (e.g., within a microfluidic channel, a drop, a free-standing liquid film, etc.). In such cases, the chemical field and the hydrodynamic flow associated with an active colloid are influenced by any nearby confining surfaces, and these disturbances couple back to the particle. Thus, an effective interaction with the spatial confinement arises. Consequently, the particle is endowed with means to perceive and to respond to its environment. Understanding these effective interactions, finding the key parameters which control them, and designing particles with desired, preconfigured responses to given environments, require interdisciplinary approaches which synergistically integrate methods and knowledge from physics, chemistry, engineering, and materials science. Here we review how, via simple models of chemical activity and self-phoretic motion, progress has recently been made in understanding the basic physical principles behind the complex behaviors exhibited by active particles near interfaces. First, we consider the occurrence of "interface-bounded" steady states of chemically active colloids near simple, nonresponsive interfaces. Examples include particles "sliding" along, or "hovering" above, a hard planar wall while inducing hydrodynamic flow of the solution. These states lay the foundations for concepts like the guidance of particles by the topography of the wall. We continue to discuss responsive interfaces: a suitable chemical patterning of a planar wall allows one to bring the particles into states of motion which are spatially localized (e.g., within chemical stripes or along chemical steps). These occur due to the wall responding to the activity-induced chemical gradients by generating osmotic flows, which encode the surface-chemistry of the wall. Finally, we discuss how, via activity-induced Marangoni stresses, long-ranged effective interactions emerge from the strong hydrodynamic response of fluid interfaces. These examples highlight how in this context a desired behavior can be potentially selected by tuning suitable parameters (e.g., the phoretic mobility of the particle, or the strength of the Marangoni stress at an interface). This can be accomplished via a judicious design of the surface chemistry of the particle and of the boundary, or by the choice of the chemical reaction in solution.

Effective squirmer models for self-phoretic chemically active spherical colloids

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

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

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

Perils of ad hoc approximations for the activity function of chemically powered colloids

Colloids can achieve motility by promoting at their surfaces chemical reactions in the surrounding solution. A well-studied case is that of self-phoresis, in which motility arises due to the spatial inhomogeneities in the chemical composition of the solution and the distinct interactions of the solvent molecules and of the reaction products with the colloid. For simple models of such chemically active colloids, the steady-state motion in an unbounded solution can be derived analytically in closed form. In contrast, for such chemically active particles moving in the vicinity of walls, the derivation of closed-form and physically intuitive solutions of the equations governing their dynamics turns out to be a severe challenge even for simple models. Therefore, recent studies of these phenomena have employed numerical methods as well as approximate analytical approaches based on multipolar expansions. We discuss and clarify certain conceptual aspects concerning the latter type of approach, which arise due to ad hoc truncations of the underlying so-called activity function, which describes the distribution of chemical reactions across the surface of the particle.

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a "swimmer efficiency" functional η is introduced. It is proven that in order to obtain maximum swimmer efficiency, the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.

Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents

Polar solvents like water support the bulk dissociation of themselves and their solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., H₂O₂ ⇌ H⁺ + HO₂^-. Using continuum theory, we study the influence of these association-dissociation reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers). We find that association-dissociation reactions should have a strong influence on swimmers' behaviour, and therefore should be included in future modelling. In particular, such bulk reactions should permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 85, 020401]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely-thin-screening-length approximation used by previous analytical theories. We identify significant departures from this limiting behaviour for micron-sized swimmers under typical experimental conditions and find that the approximation fails entirely for nanoscale swimmers.

Collective dynamics of chemically active particles trapped at a fluid interface

Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of spherically symmetric active particles trapped at a fluid-fluid interface. To this end we consider a model for the large-scale spatial distribution of particles which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction.

Self-Propulsion Mechanism of Active Janus Particles in Near-Critical Binary Mixtures

Gold-capped Janus particles immersed in a near-critical binary mixture can be propelled using illumination. We employ a nonisothermal diffuse interface approach to investigate the self-propulsion mechanism of a single colloid. We attribute the motion to body forces at the edges of a micronsized droplet that nucleates around the particle. Thus, the often-used concept of a surface velocity cannot account for the self-propulsion. The particle's swimming velocity is related to the droplet shape and size, which is determined by a so-called critical isotherm. Two distinct swimming regimes exist, depending on whether the droplet partially or completely covers the particle. Interestingly, the dependence of the swimming velocity on temperature is nonmonotonic in both regimes.