Casimir effect in active matter systems

Driving dynamic colloidal assembly using eccentric self-propelled colloids

Designing protocols to dynamically direct the self-assembly of colloidal particles has become an important direction in soft matter physics because of promising applications in the fabrication of dynamic responsive functional materials. Here, using computer simulations, we found that in the mixture of passive colloids and eccentric self-propelled active particles, when the eccentricity and self-propulsion of active particles are high enough, the eccentric active particles can push passive colloids to form a large dense dynamic cluster, and the system undergoes a novel dynamic demixing transition. Our simulations show that the dynamic demixing occurs when the eccentric active particles move much faster than the passive particles such that the dynamic trajectories of different active particles can overlap each other while passive particles are depleted from the dynamic trajectories of active particles. Our results suggest that this is in analogy to the entropy-driven demixing in colloid-polymer mixtures, in which polymer random coils can overlap with each other while depleting the colloids. More interestingly, we find that by fixing the passive colloid composition at a certain value with increasing density, the system undergoes an intriguing re-entrant mixing, and the demixing only occurs within a certain intermediate density range. This suggests a new way of designing active matter to drive the self-assembly of passive colloids and fabricate dynamic responsive materials.

Collective motion of predictive swarms

Theoretical models of populations and swarms typically start with the assumption that the motion of agents is governed by the local stimuli. However, an intelligent agent, with some understanding of the laws that govern its habitat, can anticipate the future, and make predictions to gather resources more efficiently. Here we study a specific model of this kind, where agents aim to maximize their consumption of a diffusing resource, by attempting to predict the future of a resource field and the actions of other agents. Once the agents make a prediction, they are attracted to move towards regions that have, and will have, denser resources. We find that the further the agents attempt to see into the future, the more their attempts at prediction fail, and the less resources they consume. We also study the case where predictive agents compete against non-predictive agents and find the predictors perform better than the non-predictors only when their relative numbers are very small. We conclude that predictivity pays off either when the predictors do not see too far into the future or the number of predictors is small.

Effective potentials induced by self-assembly of patchy particles

Effective colloid-colloid interactions can be tailored through the addition of a complex cosolute. Here we investigate the case of a cosolute made by self-assembling patchy particles. Depending on the valence, these particles can form either polymer chains or branched structures. We numerically calculate the effective potential Veff between two colloids immersed in a suspension of reversible patchy particles, exploring a wide region of the cosolute phase diagram and the role of valence. In addition to well-known excluded volume and depletion effects, we find that, under appropriate conditions, Veff is completely attractive but shows an oscillatory character. In the case of polymerizing cosolute, this results from the fact that chains are efficiently confined by the colloids through the onset of local order. This argument is then generalized to the case of particles with higher valence, under the condition that they are still able to maintain a fully bonded organization upon confinement. The resulting effective potentials are relevant for understanding the behavior of complex mixtures in crowded environments, but may also be exploited for tuning colloidal self-assembly at preferred target distances in order to build desired superstructures.

Fluctuation spectra and force generation in nonequilibrium systems

Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Discontinous change from thermally- to geometrically-dominated effective interactions in colloidal solutions

We report numerical results for the effective potential arising between two colloids immersed in a self-assembling cosolute which forms reversible clusters. The potential is evaluated at cosolute state points with different densities and temperatures but with the same connectivity properties. We find that the range of the resulting effective potential is controlled only by the cosolute thermal correlation length rather than by its connectivity length. We discuss the significant differences from previous results focusing on the cosolute forming irreversible clusters and we show that the irreversible bond case represents a singular limit which cannot be accessed in equilibrium by continuously increasing the bond lifetime.

Depletion forces on circular and elliptical obstacles induced by active matter

Depletion forces exerted by self-propelled particles on circular and elliptical passive objects are studied using numerical simulations. We show that a bath of active particles can induce repulsive and attractive forces which are sensitive to the shape and orientation of the passive objects (either horizontal or vertical ellipses). The resultant force on the passive objects due to the active particles is studied as a function of the shape and orientation of the passive objects, magnitude of the angular noise, and distance between the passive objects. By increasing the distance between obstacles the magnitude of the repulsive depletion force increases, as long as such a distance is less than one active particle diameter. For longer distances, the magnitude of the force always decreases with increasing distance. We also found that attractive forces may arise for vertical ellipses at high enough area fraction.

Active Brownian particles and run-and-tumble particles separate inside a maze

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

Fluctuation-induced forces between rings threaded around a polymer chain under tension

We characterize the fluctuation properties of a polymer chain under external tension and the fluctuation-induced forces between two ring molecules threaded around the chain. The problem is relevant in the context of fluctuation-induced forces in soft-matter systems, features of liquid interfaces, and to describe the properties of polyrotaxanes and slide-ring materials. We perform molecular-dynamics simulations of the Kremer-Grest bead-spring model for the polymer and a simple ring-molecule model in the canonical ensemble. We study transverse fluctuations of the stretched chain as a function of chain stretching and in the presence of ring-shaped threaded molecules. The fluctuation spectra of the chains are analyzed in equilibrium at constant temperature, and the differences in the presence of two-ring molecules are compared. For the rings located at fixed distances, we find an attractive fluctuation-induced force between the rings, proportional to the temperature and decaying with the ring distance. We characterize this force as a function of ring distance, chain stretching, and ring radius, and we measure the differences between the free chain spectrum and the fluctuations of the chain constrained by the rings. We also compare the dependence and range of the force found in the simulations with theoretical models coming from different fields.

Activity-assisted self-assembly of colloidal particles

We outline a basic strategy of how self-propulsion can be used to improve the yield of a typical colloidal self-assembly process. The success of this approach is predicated on the thoughtful design of the colloidal building block as well as how self-propulsion is endowed to the particle. As long as a set of criteria are satisfied, it is possible to significantly increase the rate of self-assembly, and greatly expand the window in parameter space where self-assembly can occur. In addition, we show that by tuning the relative on-off time of the self-propelling force it is possible to modulate the effective speed of the colloids allowing for further optimization of the self-assembly process.

Active micromachines: Microfluidics powered by mesoscale turbulence

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.

Ideal bulk pressure of active Brownian particles

The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here, we study the simplest model, an ideal gas of noninteracting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such a local pressure exists, and we show that its bulk value differs from the mechanical pressure exerted on the walls of the system. We attribute this difference to the fact that the local pressure in the bulk does not depend on boundary effects, contrary to the mechanical pressure. We carefully examine these boundary effects using a channel geometry, and we show a virial formula for the pressure correctly predicts the mechanical pressure even in finite channels. However, this result no longer holds in more complex geometries, as exemplified for a channel that includes circular obstacles.

Nonadditivity of critical Casimir forces

In soft condensed matter physics, effective interactions often emerge due to the spatial confinement of fluctuating fields. For instance, microscopic particles dissolved in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of the solvent close to its critical demixing point. These forces are theoretically predicted to be nonadditive on the scale set by the bulk correlation length of the fluctuations. Here we provide direct experimental evidence of this fact by reporting the measurement of the associated many-body forces. We consider three colloidal particles in optical traps and observe that the critical Casimir force exerted on one of them by the other two differs from the sum of the forces they exert separately. This three-body effect depends sensitively on the distance from the critical point and on the chemical functionalisation of the colloid surfaces.

The critical Casimir force, rising from fluctuating field confined between surfaces, is predicted to be nonadditive, but there is no experimental verification to date. Here the authors provide data support by quantifying the forces between three interacting colloidal particles using holographic traps.

Pressure of a gas of underdamped active dumbbells

The pressure exerted on a wall by a gas at equilibrium does not depend on the shape of the confining potential defining the walls. In contrast, it has been shown recently [A. P. Solon et al., Nat. Phys. 11, 673 (2015)] that a gas of overdamped active particles exerts on a wall a force that depends on the confining potential, resulting in a net force on an asymmetric wall between two chambers at equal densities. Here, considering a model of underdamped self-propelled dumbbells in two dimensions, we study how the behavior of the pressure depends on the damping coefficient of the dumbbells, thus exploring inertial effects. We find in particular that the force exerted on a moving wall between two chambers at equal density continuously vanishes at low damping coefficient, and exhibits a complex dependence on the damping coefficient at low density, when collisions are scarce. We further show that this behavior of the pressure can to a significant extent be understood in terms of the trajectories of individual particles close to and in contact with the wall.

Electrostatic potential of mean force between two curved surfaces in the presence of counterion connectivity

In this paper, we investigate effects of counterion connectivity (i.e., association of the counterions into a chain molecule) on the electrostatic potential of mean force (EPMF) between two similarly charged cylinder rods in a primitive model electrolyte solution by solving a classical density functional theory. The main findings include the following: (i) The counterion connectivity helps in inducing a like-charge-attractionlike (LCA-like) phenomenology even in a monovalent counterion solution wherein the LCA-like observation generally does not occur without the counterion connectivity. (ii) For divalent counterion solutions, the counterion connectivity can reinforce or weaken the LCA-like observation depending on the chain length N, and simply increases the equilibrium nearest surface separation of the rods corresponding to the minimum EPMF to nearly three times the counterion site diameter, whether N is large or small. (iii) If N is large enough, the LCA-like strength tends to be negatively correlated with the electrolyte concentration c over the entire range of the rod surface charge magnitude |σ*| considered; whereas if N drops, the correlation tends to become positive with decrease of the |σ*| value, and particularly for modest |σ*| values, the correlation relationship exhibits an extreme value phenomenon. (iv) In the case of a 1:1 electrolyte, the EPMF effects of the diameters of counterion and coion sites are similar in both situations with and without the counterion connectivity. All of these findings can be explained self-consistently by a recently proposed hydrogen-bonding style mechanism reinforced by one additional concept: flexibility of the counterion chain and the factors affecting it, like N and counterion site valence.

Swim pressure on walls with curves and corners

The concept of swim pressure quantifies the average force exerted by microswimmers on confining walls in nonequilibrium. Here we explore how the swim pressure depends on the wall curvature and on the presence of sharp corners in the wall. For active Brownian particles at high dilution, we present a coherent framework which describes the force and torque on passive particles of arbitrary shape, in the limit of large particles compared to the persistence length of the swimmer trajectories. The resulting forces can be used to derive, for example, the activity-induced depletion interaction between two disks, as well as to optimize the shape of a tracer particle for high swimming velocity. Our predictions are verifiable in experiments on passive obstacles exposed to a bath of bacteria or artificial microswimmers.

Anomalous dynamics of an elastic membrane in an active fluid

Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multifolded states, whereas stiff membranes fluctuate between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the microscale.

Tunable long range forces mediated by self-propelled colloidal hard spheres

Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.

Activity-induced phase separation and self-assembly in mixtures of active and passive particles

We investigate the phase behavior and kinetics of a monodisperse mixture of active (i.e., self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the active component triggers phase separation into a dense and a dilute phase; in the dense phase, we further find active-passive segregation, with "rafts" of passive particles in a "sea" of active particles. We find that phase separation from an initially disordered mixture can occur with as little as 15% of the particles being active. Finally, we show that a system prepared in a suitable fully segregated initial state reproducibly self-assembles an active "corona," which triggers crystallization of the passive core by initiating a compression wave. Our findings are relevant to the experimental pursuit of directed self-assembly using active particles.

Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary

We study the dynamics of nonaligning, noninteracting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the box, particles stay on the boundary and align with the local boundary normal. It is then possible to derive the steady-state density on the boundary for arbitrary box shapes. In nonconvex boxes, the nonuniqueness of the boundary normal results in hysteretic dynamics and the density is nonlocal, i.e., it depends on the global geometry of the box. These findings establish a general connection between the geometry of a confining box and the behavior of an ideal active gas it confines, thus providing a powerful tool to understand and design such confinements.

Activity-induced collapse and reexpansion of rigid polymers

We study the elastic properties of a rigid filament in a bath of self-propelled particles. We find that while fully flexible filaments swell monotonically upon increasing the strength of the propelling force, rigid filaments soften for moderate activities, collapse into metastable hairpins for intermediate strengths, and eventually reexpand when the strength of the activity of the surrounding fluid is large. This collapse and reexpansion of the filament with the bath activity is reminiscent of the behavior observed in polyelectrolytes in the presence of different concentrations of multivalent salt.

Curvature-induced activation of a passive tracer in an active bath

We use numerical simulations to study the motion of a large asymmetric tracer immersed in a low-density suspension of self-propelled particles in two dimensions. Specifically, we analyze how the curvature of the tracer affects its translational and rotational motion in an active environment. We find that even very small amounts of curvature are sufficient for the active bath to impart directed motion to the tracer, which results in its effective activation. We propose simple scaling arguments to characterize this induced activity in terms of the curvature of the tracer and the strength of the self-propelling force. Our results suggest new ways of controlling the transport properties of passive tracers in an active medium by carefully tailoring their geometry.