Dynamics and risk sharing in groups of selfish individuals.

Understanding why animals organize in collective states is a central question of current research in, e.g., biology, physics, and psychology. More than 50 years ago, W.D. Hamilton postulated that the formation of animal herds may simply result from the individual's selfish motivation to minimize their predation risk. The latter is quantified by the domain of danger (DOD) which is given by the Voronoi area around each individual. In fact, simulations show that individuals aiming to reduce their DODs form compact groups similar to what is observed in many living systems. However, despite the apparent simplicity of this problem, it is not clear what motional strategy is required to find an optimal solution. Here, we use the framework of Multi Agent Reinforcement Learning (MARL) which gives the unbiased and optimal strategy of individuals to solve the selfish herd problem. We demonstrate that the motivation of individuals to reduce their predation risk naturally leads to pronounced collective behaviors including the formation of cohesive swirls. We reveal a previously unexplored rather complex intra-group motion which eventually leads to a evenly shared predation risk amongst selfish individuals.

How are mobility and friction related in viscoelastic fluids?

The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and, thereby, relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model, and hard spheres treated by mode coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration.

Barrier Crossing in a Viscoelastic Bath.

We investigate the hopping dynamics of a colloidal particle across a potential barrier and within a viscoelastic, i.e., non-Markovian, bath and report two clearly separated timescales in the corresponding waiting time distributions. While the longer timescale exponentially depends on the barrier height, the shorter one is similar to the relaxation time of the fluid. This short timescale is a signature of the storage and release of elastic energy inside the bath that strongly increases the hopping rate. Our results are in excellent agreement with numerical simulations of a simple Maxwell model.

Force Generation in Confined Active Fluids: The Role of Microstructure.

We experimentally determine the force exerted by a bath of active particles onto a passive probe as a function of its distance to a wall and compare it to the measured averaged density distribution of active particles around the probe. Within the framework of an active stress, we demonstrate that both quantities are-up to a factor-directly related to each other. Our results are in excellent agreement with a minimal numerical model and confirm a general and system-independent relationship between the microstructure of active particles and transmitted forces.

Erratum: Autonomously Probing Viscoelasticity in Disordered Suspensions [Phys. Rev. Lett. 125, 258002 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.125.258002.

Critical Casimir interactions of colloids in micellar critical solutions.

We study the temperature-dependence of critical Casimir interactions in a critical micellar solution of the nonionic surfactant C12E5 dissolved in water. Experimentally, this is achieved with total internal reflection microscopy (TIRM) which measures the interaction between a single particle and a flat wall. For comparison, we also studied the pair interactions of a two dimensional layer of colloidal particles in the identical micellar system which yields good agreement with the TIRM results. Although, at the surfactant concentration considered here, the fluid forms a dynamical network of wormlike micelles whose structure is considerably more complex than that of simple critical molecular fluids, the temperature-dependence of the measured interactions is - for surface-to-surface distances above 160 nm - in excellent quantitative agreement with theory. Below 160 nm, deviations arise which we attribute to the adsorption of micelles to the interacting surfaces.

Active colloids under geometrical constraints in viscoelastic media.

We study the behavior of active particles (APs) moving in a viscoelastic fluid in the presence of geometrical confinements. Upon approaching a flat wall, we find that APs slow down due to compression of the enclosed viscoelastic fluid. In addition, they receive a viscoelastic torque leading to sudden orientational changes and departure from walls. Based on these observations, we develop a numerical model which can also be applied to other geometries and yields good agreement with experimental data. Our results demonstrate, that APs are able to move through complex geometrical structures more effectively when suspended in a viscoelastic compared to a Newtonian fluid.

Two step micro-rheological behavior in a viscoelastic fluid.

We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.

Active particles sense micromechanical properties of glasses.

Understanding the mechanical properties of glasses is a great scientific challenge. A powerful technique to study the material response on a microscopic scale is microrheology, in which one analyses the translational dynamics of an externally driven probe particle. Here we show that the translational and rotational dynamics of a self-propelled probe particle with an unconstrained orientational motion can be used to gather information about the mechanical properties of a colloidal glassy system. We find that its rotational diffusion coefficient continuously increases towards the glass transition and drops down in the glassy state. Such unexpected behaviour demonstrates a strong coupling mechanism between the orientation of the active probe particle and the glassy structure, which can be well described by a simple rheological model. Our results suggest that active probe particles may be useful for the micromechanical characterization of complex materials.

Autonomously Probing Viscoelasticity in Disordered Suspensions.

Recent experiments show a strong rotational diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.

Propagating density spikes in light-powered motility-ratchets.

Combining experiments and computer simulations, we use a spatially periodic and flashing light-field to direct the motion of phototactic active colloids. Here, the colloids self-organize into a density spike pattern, which resembles a shock wave and propagates over long distances, almost without dispersing. The underlying mechanism involves a synchronization of the colloids with the light-field, so that particles see the same intensity gradient each time the light-pattern is switched on, but no gradient in between (for example). This creates pulsating transport whose strength and direction can be controlled via the flashing protocol and the self-propulsion speed of the colloids. Our results might be useful for drug delivery applications and can be used to segregate active colloids by their speed.

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast.

We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity, and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

Chemotaxis of Active Janus Nanoparticles.

While colloids and molecules in solution exhibit passive Brownian motion, particles that are partially covered with a catalyst, which promotes the transformation of a fuel dissolved in the solution, can actively move. These active Janus particles are known as "chemical nanomotors" or self-propelling "swimmers" and have been realized with a range of catalysts, sizes, and particle geometries. Because their active translation depends on the fuel concentration, one expects that active colloidal particles should also be able to swim toward a fuel source. Synthesizing and engineering nanoparticles with distinct chemotactic properties may enable important developments, such as particles that can autonomously swim along a pH gradient toward a tumor. Chemotaxis requires that the particles possess an active coupling of their orientation to a chemical gradient. In this Perspective we provide a simple, intuitive description of the underlying mechanisms for chemotaxis, as well as the means to analyze and classify active particles that can show positive or negative chemotaxis. The classification provides guidance for engineering a specific response and is a useful organizing framework for the quantitative analysis and modeling of chemotactic behaviors. Chemotaxis is emerging as an important focus area in the field of active colloids and promises a number of fascinating applications for nanoparticles and particle-based delivery.

Memory-Induced Transition from a Persistent Random Walk to Circular Motion for Achiral Microswimmers.

We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persistent rotational motion above a critical propulsion speed, despite their spherical shape and stiffness. We observe that, in contrast to chiral asymmetric microswimmers, the resulting circular orbits can spontaneously reverse their sense of rotation and exhibit an angular velocity and a radius of curvature that nonlinearly depend on the propulsion speed. By means of a minimal non-Markovian Langevin model for active Brownian motion, we show that these nonequilibrium effects emerge from the delayed response of the fluid with respect to the self-propulsion of the particle without counterpart in Newtonian fluids.

Dynamics of Self-Propelled Janus Particles in Viscoelastic Fluids.

We experimentally investigate active motion of spherical Janus colloidal particles in a viscoelastic fluid. Self-propulsion is achieved by a local concentration gradient of a critical polymer mixture which is imposed by laser illumination. Even in the regime where the fluid's viscosity is independent of the deformation rate induced by the particle, we find a remarkable increase of up to 2 orders of magnitude of the rotational diffusion with increasing particle velocity, which can be phenomenologically described by an effective rotational diffusion coefficient dependent on the Weissenberg number. We show that this effect gives rise to a highly anisotropic response of microswimmers in viscoelastic media to external forces, depending on its orientation.

Interactions of Colloidal Particles and Droplets with Water-Oil Interfaces Measured by Total Internal Reflection Microscopy.

Total internal reflection microscopy (TIRM) is a well-known technique to measure weak forces between colloidal particles suspended in a liquid and a solid surface by using evanescent light scattering. In contrast to typical TIRM experiments, which are carried out at liquid-solid interfaces, here we extend this method to liquid-liquid interfaces. Exemplarily, we demonstrate this concept by investigating the interactions of micrometer-sized polystyrene particles and oil droplets near a flat water-oil interface for different concentrations of added salt and ionic surfactant (SDS). We find that the interaction is well described by the superposition of van der Waals and double layer forces. Interestingly, the interaction potentials are, within the SDS concentration range studied here, rather independent of the surfactant concentration, which suggests a delicate counter play of different interactions at the oil-water interface and provides interesting insights into the mechanisms relevant for the stability of emulsions.

Direct measurement of thermophoretic forces.

We study the thermophoretic motion of a micron sized single colloidal particle in front of a flat wall by evanescent light scattering. To quantify thermophoretic effects we analyse the nonequilibrium steady state (NESS) of the particle in a constant temperature gradient perpendicular to the confining walls. We propose to determine thermophoretic forces from a "generalized potential" associated with the probability distribution of the particle position in the NESS. Experimentally we demonstrate, how this spatial probability distribution is measured and how thermophoretic forces can be extracted with 10 fN resolution. By varying temperature gradient and ambient temperature, the temperature dependence of Soret coefficient ST(T) is determined for r = 2.5 µm polystyrene and r = 1.35 µm melamine particles. The functional form of ST(T) is in good agreement with findings for smaller colloids. In addition, we measure and discuss hydrodynamic effects in the confined geometry. The theoretical and experimental technique proposed here extends thermophoresis measurements to so far inaccessible particle sizes and particle solvent combinations.

Effect of confinement on the mode dynamics of dipole clusters.

Dynamical properties of colloidal clusters composed of paramagnetic beads are presented. The clusters were trapped either in a parabolic trough or in a hard-wall confinement. In order to access the dynamics of the ensembles, the instantaneous normal mode (INM) approach is utilized, which uses cluster configurations as an input. The peaks in the mode spectra weaken when the system size is increased and when the coupling strength is lowered. The short-time diffusive properties of the clusters are deduced using the INM technique. It is found that angular diffusion is always larger than radial diffusion regardless of the shape of the external trap. Further, short-time diffusion seems to be almost independent of the coupling strength in the solid regime, but decreases with increasing packing fraction and size of the ensembles. In general, it is found that diffusion is larger for parabolically confined than for hard-wall trapped clusters.

Formation, compression and surface melting of colloidal clusters by active particles.

We demonstrate with experiments and numerical simulations that the structure and dynamics of a suspension of passive particles is strongly altered by adding a very small (<1%) number of active particles. With increasing passive particle density, we observe first the formation of dynamic clusters comprised of passive particles being surrounded by active particles, then the merging and compression of these clusters, and eventually the local melting of crystalline regions by enclosed active particles.