Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

Electro-osmosis in nematic liquid crystals.

We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. We verify the model by comparing its predictions to the results of the experiments on the substrate-controlled liquid-crystal-enabled electrokinetics. In the experiments, a nematic liquid crystal confined to a thin planar cell with surface-patterned anchoring conditions exhibits electro-osmotic flows along the "guiding rails" imposed by the spatially varying director. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full set of nematic viscosities.

Publisher's Note: Colloidal interactions in a homeotropic nematic cell with different elastic constants [Phys. Rev. E 92, 042505 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.92.042505.

Colloidal interactions in a homeotropic nematic cell with different elastic constants.

We propose a theoretical description of the interaction mediated by a nematic-liquid-crystal host with different Frank elastic constants. A general expression for the energy of such an interaction between colloidal particles of arbitrary size and shape suspended in a homeotropic cell is obtained. In the cells of large thickness, the presented potential converges to that found previously for small particles in the nematic bulk. In general, our results confirm the validity of the one-constant approximation for weakly elastically anisotropic nematic liquid crystals. For nematics with a high splay-to-bend ratio we predict a larger range of the interaction. Using the dependence of this range on the elastic constants, we show that there exists a qualitative similarity between the interactions in a nematic and in a smectic-A phase. It manifests itself, in particular, in a decrease of the angle between a chain of quadrupole particles and the uniform far-field director across a nematic-smectic-A phase transition. We also demonstrate that the anisotropy of the elastic constants can lead to the formation of thermodynamically stable linear superstructures of asymmetric particles (elastic monopoles) with large, compared to usual dipole chains, interparticle distances.

Surface-induced structures in nematic liquid crystal colloids.

We predict theoretically the existence of a class of colloidal structures in nematic liquid crystal (NLC) cells, which are induced by surface patterns on the plates of the cell (like cells with UV-irradiated polyamide surfaces using micron sized masks in front of the cell). These bulk structures arise from nonuniform boundary conditions for the director distortions at the confining surfaces. In particular, we demonstrate that quadrupole spherical particles (like spheres with boojums or Saturn-ring director configurations) form a square lattice inside a planar NLC cell, which has checkerboard patterns on both its plates.

Elastic octopoles and colloidal structures in nematic liquid crystals.

We propose a simple theoretical model which explains the formation of dipolar two- (2D) and three-dimensional (3D) colloidal structures in nematic liquid crystals. The colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole, and octopole moments. It is shown that the octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption to the case of an external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently.

Interaction of small spherical particles in confined cholesteric liquid crystals.

The theory of the elastic interaction of spherical colloidal particles immersed into a confined cholesteric liquid crystal is proposed. The case of weak anchoring on the particle surfaces is considered. We derive a general expression for the energy of the interaction between small spherical particles (with diameter much smaller than the cholesteric pitch) suspended in a cholesteric confined by two parallel planes. The resulting form of the interaction energy has a more complex spatial pattern and energy versus distance dependence than that in nematic colloids. The absence of translational symmetry related to helical periodicity and local nematic ordering in cholesteric liquid crystals manifest themselves in the complex nature of the interaction maps.

Peculiarity of the interaction of small particles in smectic liquid crystals.

We investigate the peculiarity of the interaction between particles immersed into a smectic liquid crystal with a layered structure. Such a structure of a liquid crystal imposes restrictions on possible deformations of the layer displacement field. Previous studies neglect this fact and give improper results for the interaction potential within one molecular layer. The present paper shows that such restrictions yield an interaction potential substantially different from those of previous studies. Oscillatory behavior, which was not present in the potentials of previous studies, might give rise to superstructures of immersed particles with finite interparticle distance.

Theory of elastic interaction between colloidal particles in a nematic cell in the presence of an external electric or magnetic field.

The Green's function method developed previously [S. B. Chernyshuk and B. I. Lev, Phys. Rev. E 81, 041701 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in a nematic cell in the presence of an external electric or magnetic field. Formulas for dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of predictions has been made: (1) The deconfinement effect for dipole particles in the homeotropic nematic cell when an electric field is approaching its Freedericksz threshold value E⇒E(t). This means cancellation of the confinement effect found in [M. Vilfan et al., Phys. Rev. Lett. 101, 237801 (2008)] near the Freedericksz transition. In the planar nematic cell this deconfinement effect exists for both dipole and quadrupole particles and depends on the field orientation as well as on the sign of dielectric anisotropy Δε. (2) The effect of tunable stabilization of the particles is predicted. The equilibrium distance between two particles, which are attracted along the electric field parallel to the planes of a homeotropic nematic cell with Δε<0, depends on the strength of the field. (3) Attraction and repulsion zones for all elastic interactions are changed dramatically under the action of the external field.

Theory of elastic interaction between arbitrary colloidal particles in confined nematic liquid crystals.

We develop the method proposed by Chernyshuk and Lev [Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of elastic interactions between colloidal particles of arbitrary shape and chirality (polar as well as azimuthal anchoring) in the confined nematic liquid crystal (NLC). General expressions for six different types of multipole elastic interactions are obtained in the confined NLC: monopole-monopole (Coulomb type), monopole-dipole, monopole-quadrupole, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions. The obtained formulas remain valid in the presence of the external electric or magnetic fields. The exact equations are found for all multipole coefficients for the weak anchoring case. For the strong anchoring coupling, the connection between the symmetry of the shape or director and multipole coefficients is obtained, which enables us to predict which multipole coefficients vanish and which remain nonzero. The particles with azimuthal helicoid anchoring are considered as an example. Dipole-dipole interactions between helicoid cylinders and cones are found in the confined NLC. In addition, the banana-shaped particles in homeotropic and planar nematic cells are considered. It is found that the dipole-dipole interaction between banana-shaped particles differs greatly from the dipole-dipole interaction between the axially symmetrical particles in the nematic cell. There is a crossover from attraction to repulsion between banana particles along some directions in nematic cells. It is shown that monopoles do not "feel" the type of nematic cell: monopole-monopole interaction turns out to be the same in homeotropic and planar nematic cells and converges to the Coulomb law as thickness increases, L→∞.