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.
Using numerical simulations, we study how a solution of small active disks, acting as depletants, induces effective interactions on large passive colloids. Specifically, we analyze how the range, strength, and sign of these interactions are crucially dependent on the shape of the colloids. Our findings indicate that while colloidal rods experience a long-ranged predominantly attractive interaction, colloidal disks feel a repulsive force that is short-ranged in nature and grows in strength with the size ratio between the colloids and active depletants. For colloidal rods, simple scaling arguments are proposed to characterize the strength of these induced interactions.
We use numerical simulations to study the phase behavior of self-propelled spherical and dumbbellar particles interacting via micro-phase separation inducing potentials. Our results indicate that under the appropriate conditions, it is possible to drive the formation of two new active states; a spinning cluster crystal, i.e. an ordered mesoscopic phase having finite size spinning crystallites as lattice sites, and a fluid of living clusters, i.e. a two dimensional fluid where each "particle" is a finite size living cluster. We discuss the dynamics of these phases and suggest ways of extending their stability under a wide range of active forces. INTRODUCTIONSpontaneous pattern formation is a ubiquitous phenomenon in nature and arises in both equilibrium and out-ofequilibrium systems. Apart from the many biological examples [1,2], important synthetic systems such as colloids and block copolymers have been shown to exhibit complex spatial equilibrium patterns upon self-assembly. Control of patterns at the micro and nanoscale is integral to the development of materials with novel optical, electrical, and rheological properties [3].One route to spontaneous pattern formation in equilibrium systems is achieved via micro-phase separation [4], a phenomenon that typically occurs when geometrical or chemical constraints prevent a system from fully phase separating. Block copolymers, for instance, exhibit a wide variety of patterns upon micro-phase separation that can be controlled by tuning the relative length of the two blocks, from lamellae to cylinders to networks [5][6][7]. An alternative route is achieved with competing interactions. In colloidal supensions, for instance, the interplay between a short range attraction and a long range repulsion has been shown to lead to micro-phase separation into a variety of patterns [8] with symmetry dependent on the relative weight of the two interactions [9][10][11][12][13]. In these cases, the short range attraction is usually induced by depletion, hydrophobic or van der Waals forces, while the long range repulsion may come from dipolar forces or screened electrostatics [14][15][16][17].Recent experiments in two dimensions have shown that dilute suspensions of self-propelled colloidal particles can self-assemble into "dynamic", "living" crystals [18][19][20], where finite-sized aggregates continually join, break apart, dissolve, and reform. In this case, what limits the growth of the crystal to a macroscopic size − the scenario that would be favored due to inter-particle attractive interactions − is the self-propulsion of the active particles. This behavior seems to be specific to spherical particles, as these are able to freely re-orient within the developing crystallites under the influence of thermal forces, thus creating large stresses within the crystal. The formation of living clusters has also been recently observed in computer simulations of a three dimensional diluted suspension of self-propelled attractive spheres [21,22]; however, in three dimensions clusters did not ...
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