Microswimmers Knead Nematics into Cholesterics.

The hydrodynamic stresses created by active particles can destabilize orientational order present in the system. This is manifested, for example, by the appearance of a bend instability in active nematics or in quasi-two-dimensional living liquid crystals consisting of swimming bacteria in thin nematic films. Using large-scale hydrodynamics simulations, we study a system consisting of spherical microswimmers within a three-dimensional nematic liquid crystal. We observe a spontaneous chiral symmetry breaking, where the uniform nematic state is kneaded into a continuously twisting state, corresponding to a helical director configuration akin to a cholesteric liquid crystal. The transition arises from the hydrodynamic coupling between the liquid crystalline elasticity and the swimmer flow fields, leading to a twist-bend instability of the nematic order. It is observed for both pusher (extensile) and puller (contractile) swimmers. Further, we show that the liquid crystal director and particle trajectories are connected: in the cholesteric state the particle trajectories become helicoidal.

Collective Flows Drive Cavitation in Spinner Monolayers.

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced.

Anomalous Diffusion of Deformable Particles in a Honeycomb Network.

Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusionlike transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, due to long memory. This leads to a lateral ballistic drift in the network at small concentration and anomalous superdiffusion at larger concentration, even though the network is ordered. A further increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle anomalous diffusion into a classical diffusion. We expect the drifting and diffusive regime transition to be generic for deformable particles.

Sorting and Extraction of Self-Propelled Chiral Particles by Polarized Wall Currents.

The dynamics of self-propelled particles with curved trajectories is investigated. Two modes are observed, a bulk mode with a quasicircular motion and a surface mode with the particles following the walls. The surface mode is the only mode of ballistic transport and the particle current is polar and depends on the particles' chirality. We show that a robust sorting and extraction occurs when the particles explore a domain with two exit gates collecting selectively the particles circling left and right. With a counterslope, the extraction rate is found to increase while the sorting error is reduced.

Two-Phase Crystallization in a Carpet of Inertial Spinners.

We study the dynamics of torque driven spherical spinners settled on a surface, and demonstrate that hydrodynamic interactions at finite Reynolds numbers can lead to a concentration dependent and nonuniform crystallization. At semidilute concentrations, we observe a rapid formation of a uniform hexagonal structure in the spinner monolayer. We attribute this to repulsive hydrodynamic interactions created by the secondary flow of the spinning particles. Increasing the surface coverage leads to a state with two coexisting spinner densities. The uniform hexagonal structure deviates into a high density crystalline structure surrounded by a continuous lower density hexatically ordered state. We show that this phase separation occurs due to a nonmonotonic hydrodynamic repulsion, arising from a concentration dependent spinning frequency.

Characterization and control of a bottleneck-induced traffic-jam transition for self-propelled particles in a track.

A collection of self-propelled elongated particles is circulating in a circular track. Due to the presence of a bottleneck, the flow transits to a congested state for a sufficient number of particles, even if the whole track is not saturated. Both experiments and simulations are used to identify the transition toward congestion. An intermediate regime of coexistence is characterized by intermittency between a free flow state and a jammed state. The range of the coexistence region is found to depend explicitly on fluctuating quantities such as the distribution of the escape times from a jam and the headway time distribution between free particles. Optimization strategies, such as the "slower is faster" effect, are tested in experiments and simulations, and an increase in the traffic performances is reported.

Hydrodynamic self-assembly of active colloids: chiral spinners and dynamic crystals.

Active colloids self-organise into a variety of collective states, ranging from highly motile "molecules" to complex 2D structures. Using large-scale simulations, we show that hydrodynamic interactions, together with a gravity-like aligning field, lead to tunable self-assembly of active colloidal spheres near a surface. The observed structures depend on the hydrodynamic characteristics: particles driven at the front, pullers, form small chiral spinners consisting of two or three particles, whereas those driven at the rear, pushers, assemble into large dynamic aggregates. The rotational motion of the puller spinners, arises from spontaneous breaking of the internal chirality. Our results show that the fluid flow mediates chiral transfer between neighbouring spinners. Finally we show that the chirality of the individual spinners controls the topology of the self-assembly in solution: homochiral samples assemble into a hexagonally symmetric 2D crystal lattice while racemic mixtures show reduced hexatic order with diffusion-like dynamics.

A nonequilibrium force can stabilize 2D active nematics.

Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial suspensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.

Hydrodynamic interaction of a self-propelling particle with a wall : Comparison between an active Janus particle and a squirmer model.

Using lattice Boltzmann simulations we study the hydrodynamics of an active spherical particle near a no-slip wall. We develop a computational model for an active Janus particle, by considering different and independent mobilities on the two hemispheres and compare the behaviour to a standard squirmer model. We show that the topology of the far-field hydrodynamic nature of the active Janus particle is similar to the standard squirmer model, but in the near-field the hydrodynamics differ. In order to study how the near-field effects affect the interaction between the particle and a flat wall, we compare the behaviour of a Janus swimmer and a squirmer near a no-slip surface via extensive numerical simulations. Our results show generally a good agreement between these two models, but they reveal some key differences especially with low magnitudes of the squirming parameter [Formula: see text]. Notably the affinity of the particles to be trapped at a surface is increased for the active Janus particles when compared to standard squirmers. Finally, we find that when the particle is trapped on the surface, the velocity parallel to the surface exceeds the bulk swimming speed and scales linearly with [Formula: see text].

Hydrodynamic oscillations and variable swimming speed in squirmers close to repulsive walls.

We present a lattice Boltzmann study of the hydrodynamics of a fully resolved squirmer, confined in a slab of fluid between two no-slip walls. We show that the coupling between hydrodynamics and short-range repulsive interactions between the swimmer and the surface can lead to hydrodynamic trapping of both pushers and pullers at the wall, and to hydrodynamic oscillations in the case of a pusher. We further show that a pusher moves significantly faster when close to a surface than in the bulk, whereas a puller undergoes a transition between fast motion and a dynamical standstill according to the range of the repulsive interaction. Our results critically require near-field hydrodynamics and demonstrate that far-field hydrodynamics is insufficient to give even a qualitatively correct account of swimmer behaviour near walls. Finally our simulations suggest that it should be possible to control the density and speed of squirmers at a surface by tuning the range of steric and electrostatic swimmer-wall interactions.

Swimming in a crystal.

We study catalytic Janus particles and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus particles orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E. coli bacteria behave very differently in the same colloidal crystal: their circular orbits on plain glass are rectified into long, straight runs, because the bacteria are unable to turn corners inside the crystal.

Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model.

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.

Statistical temperature molecular dynamics simulations applied to phase transitions in liquid crystalline systems.

The recently developed statistical temperature molecular dynamics (STMD) method [Kim et al., Phys. Rev. Lett. 97, 050601 (2006)] is applied to the simulation of liquid crystalline soft matter systems. Results are presented demonstrating how, in combination with anisotropic soft core potentials, STMD simulation is able to sample efficiently across a large temperature window; and thus bridge across isotropic-liquid crystal phase transitions. Data is presented for two separate systems, namely, a single-site interaction model and an AB rod-coil block copolymer. The results are in excellent agreement with phase diagrams calculated by a series of traditional canonical molecular dynamics simulations bridging similar temperature/energy windows. In addition to the usual energetic and structural information, the STMD technique provides the temperature dependence of the entropy, free energy and heat capacity of the system as by-products of the single simulation. The combined soft-core/STMD strategy is presented as an effective means of scanning the phase diagram of a simple molecular interaction model to understand the relationship between molecular structure and phase behavior.

A soft-core Gay-Berne model for the simulation of liquid crystals by Hamiltonian replica exchange.

The Gay-Berne (GB) potential has proved highly successful in the simulation of liquid crystal phases, although it is fairly demanding in terms of resources for simulations of large (e.g., N>10(5)) systems, as increasingly required in applications. Here, we introduce a soft-core GB model, which exhibits both liquid crystal phase behavior and rapid equilibration. We show that the Hamiltonian replica exchange method, coupled with the newly introduced soft-core GB model, can effectively speed up the equilibration of a GB liquid crystal phase by frequent exchange of configurations between replicas, while still recovering the mesogenic properties of the standard GB potential.

A coarse-grained simulation study of mesophase formation in a series of rod-coil multiblock copolymers.

The mesophase behaviour of a rod-coil multiblock copolymer is assessed by means of a new soft-core simulation model, which is suitable for the simulation of combinations of isotropic and anisotropic particles. The simulations demonstrate the presence of isotropic melt, micelles, lamellar, nematic and gyroid phases, with ordered phases able to grow spontaneously from the isotropic melt. The influence of increasing the length of the rigid rod-component of the polymer is studied, with mesophase stability enhanced by increases in rod length. Increased nematic phase stability is demonstrated also as the length of rod component is increased. For longer rods (smaller fraction of coils) the models show evidence of metastable chevron-like structures that initially form on cooling from the polymer melt. These are eventually lost in favour of true lamellar ordering over long annealing runs. The structure of molecules within the phases formed is also assessed. Chains in the lamellar phase are shown to produce both bridging and loop behaviour, with the latter preferred slightly. Simulations at a low occupied volume fraction, corresponding to self-assembly in solution, demonstrate the formation of a structurally ordered nanowire.

A new anisotropic soft-core model for the simulation of liquid crystal mesophases.

A new anisotropic soft-core model is presented, which is suitable for the rapid simulation of liquid crystal mesophases. The potential is based on a soft spherocylinder, which can be easily tuned to favor different liquid crystal mesophases. The soft-core nature of the potential makes it suitable for long-time step molecular dynamics or dissipative particle dynamics simulations, particularly as a reference model for mesogens or as an anisotropic solvent for use in combination with atomistic models. Results are presented for two variants of the new potential, which show different mesophase behaviors. Variants of the potential can also be linked together to produce more complicated molecular structures. Here, as an example, results are provided for a model multipedal liquid crystal, which has eight liquid crystalline groups linked to a central core via semiflexible chains. Here, despite the complexity of molecular structure, the model succeeds in showing the spontaneous formation of a liquid crystal phase. The results also demonstrate that there is a very strong coupling between the internal structure of the multipedal mesogen and the molecular order of the phase, with the mesogen spontaneously undergoing major structural rearrangement at the transition to the liquid crystal phase.