Elastic and hydrodynamic torques on a colloidal disk within a nematic liquid crystal

Topological defect-propelled swimming of nematic colloids

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.

Anisotropic viscous effects of local flow by a rotating microparticle in nematic liquid crystal

The presented study opens a perspective to investigate the effects of local flow on nematic liquid crystals. A particle rotated in nematic fluids typically generates a rotationally symmetric local flow, which causes a change in the director orientation. The director above the threshold velocity has a particular angle determined by the ratio of Leslie coefficients, α_{2}/α_{3}. In 5CB liquid crystals, this director angle with respect to the flow is approximately 13^{∘}. The angle is calculated through Ericksen-Leslie theory. The angle is not dependent on rotation frequency or particle size but temperature. The area of the influenced region increases with the rotation frequency and particle size. The changes in radius of the influenced region are calculated theoretically using Ericksen number. Further, an interference pattern appears at the edge of the influenced region by the refractive indexes mismatch between the influenced region and the rest. We experimentally obtain the thickness of the influenced region analyzing intervals of the pattern.

Thermal Buckling Transition of Crystalline Membranes in a Field

Two-dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant, e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the embedding space. An example is provided by a membrane in an orientational field, tuned to a critical buckling point by application of in-plane stresses. Through a detailed analysis, we show that the transition is in a new universality class. The self-consistent screening method predicts a second-order transition, with modified anomalous elasticity exponents at criticality, while the RG suggests a weakly first-order transition.

Hindered nematic alignment of hematite spindles in poly(N-isopropylacrylamide) hydrogels: a small-angle X-ray scattering and rheology study

Field-induced changes to the mesostructure of ferrogels consisting of spindle-shaped hematite particles and poly(N-isopropylacrylamide) are investigated by means of small-angle X-ray scattering (SAXS). Related field-induced changes to the macroscopic viscoelastic properties of these composites are probed by means of oscillatory shear experiments in an external magnetic field. Because of their magnetic moment and magnetic anisotropy, the hematite spindles align with their long axis perpendicular to the direction of an external magnetic field. The field-induced torque acting on the magnetic particles leads to an elastic deformation of the hydrogel matrix. Thus, the field-dependent orientational distribution functions of anisotropic particles acting as microrheological probes depend on the elastic modulus of the hydrogel matrix. The orientational distribution functions are determined by means of SAXS experiments as a function of the varying flux density of an external magnetic field. With increasing elasticity of the hydrogels, tunedviathe polymer volume fraction and the crosslinking density, the field-induced alignment of these anisotropic magnetic particles is progressively hindered. The microrheological results are in accordance with macrorheological experiments indicating increasing elasticity with increasing flux density of an external field.

Dynamics of disk pairs in a nematic liquid crystal

We use a hybrid lattice Boltzmann method to study the behavior of sets of ferromagnetic colloidal disks in a nematic liquid crystal. When a weak rotating magnetic field acts on the system, the disks rotate following the magnetic field. This leads to a distortion in the liquid crystal that drives translational motion of the disks. If the concentration of disks is high, disks get locked together: a stable chain configuration is created, where each disk lays on the nearest neighbor. For intermediate concentrations of disks, a different behavior is observed. When disks are rotated by the magnetic field by more than 90^{∘} from their initial orientation, the distortion in the liquid crystal leads to a simultaneous flip of both disks. The final disk positions depends only weakly on the initial configuration. Consecutive rotations of magnetic field push disks towards an equidistant configuration. Periodicity of the systems studied and analysis of the flipping motion of a single disk imply that one can use weak rotating magnetic fields to create stable crystal structures of disks.

Dynamics of a disc in a nematic liquid crystal

We use lattice Boltzmann simulations to study the dynamics of a disc immersed in a nematic liquid crystal. In the absence of external torques, discs with homeotropic anchoring align with their surface normal parallel to the director of the nematic liquid crystal. In the presence of a weak magnetic field a ferromagnetic disc will rotate to equilibrate the elastic torque due to the distortion of the nematic director and the magnetic torque. When the magnetic field rotates the disc so that the angle θ between normal to the surface of the disc â and director of the liquid crystal n[combining circumflex] becomes greater than π/2, the disc flips around the axis perpendicular to the rotation axis so that â sweeps through π radians. An analysis of this behaviour was performed. In particular, we look at the impact of the disc thickness and edges on defect creation and the flipping transition. We also analyse the importance of backflow.

Anisotropic colloidal transport and periodic stick-slip motion in cholesteric finger textures

We have investigated the mobility of discoidal colloidal particles sedimenting within cholesteric finger textures formed by mixtures of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) and the chiral dopant 4-(2-methylbutyl)-4'-cyanobiphenyl (CB15) with cholesteric pitch p between 24 and 114 μm. The nickel disks, with radius 17 μm and thickness 300 nm, displayed varied transport behavior that depended on the size of the pitch and the orientation of the gravitational force with respect to the cholesteric axis. In textures with small pitch (p < 40 μm), the disks moved perpendicular to the axis irrespective of the orientation of gravity as a result of an elastic retarding force that prevented motion along the axis. In textures with larger pitch, the disks similarly moved perpendicular to the axis when the angle between the force and axis was large. When the angle was small, the disks displayed stick-slip motion caused by periodic yielding of the finger texture. A model considering viscous drag on the particles and the elastic energy cost of deforming the finger texture describes the stick-slip motion accurately. The effective drag viscosities obtained from the disk motion are anomalously large compared with those of pure nematic 5CB indicating a large contribution to the dissipation from the motion of disclinations in the texture in the vicinity of the translating disks.

Equilibrium state of a cylindrical particle with flat ends in nematic liquid crystals

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect ratios of this colloidal geometry from thin discotic to long rodlike shapes and several colloidal length scales ranging from mesoscale to nanoscale are investigated. We show that the equilibrium state of this colloidal geometry is sensitive to the two geometrical parameters: aspect ratio and length scale of the particle. For a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. Upon reducing the particle size to nanoscale, the equilibrium angle follows a descending or ascending trend in such a way that the equilibrium angle of a particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a parallel alignment with respect to the far-field nematic, whereas the equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a rodlike particle) tends toward a perpendicular alignment to the uniform nematic direction. The discrepancy between the equilibrium angles of the mesoscopic and nanoscopic particles originates from the significant differences between their defect structures. The possible defect structures related to mesoscopic and nanoscopic colloidal particles of this geometry are also introduced.

Anisotropic Stokes drag and dynamic lift on spheres sedimenting in a nematic liquid crystal

The motion of silica spheres with homeotropic anchoring sedimenting within nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) has been studied at low Ericksen number. The magnitude of the spheres' velocity depends on the angle θ between the far-field nematic director and the gravitational force, indicating an anisotropic Stokes drag. When the director is oriented at an oblique angle to the gravitational force, the velocity also acquires a component normal to the force, demonstrating the existence of a lift force generated by the fluid. The magnitude and direction of the velocity as functions of θ quantitatively obey theoretically predicted forms.