Dynamics of the refractive index in Langmuir monolayers.

We present theoretical description of dynamics of the refractive index in Langmuir monolayers subjected to continuous-wave (CW) laser radiation, using the mechanism of the local temperature fluctuations. Such mechanism can be applied to all monolayer systems that consist of rodlike molecules. The CW laser radiation induces conformational transitions of molecules in monolayer, which, after some time being in the excited state, come back into the ground state, thus renewing their initial shape and releasing energy into the medium, locally heating it. This leads to the local temperature change, which promotes new conformational transitions of molecules. Such nonlinear energy redistribution mechanism permits the conformational transition boundary to move. The existence of the transitions is seen from the change of the refractive index.

Ground state and peculiarity of particle interactions in liquid crystal colloids.

This research proposes a general approach to determine the peculiarity of the interaction between colloidal particles in different liquid crystals. The main idea of this approach is in the definition of the colloidal particle as a source of the possible deformation of the ground state of the director field distribution. The ground state imposes restrictions on possible deformations and determines the peculiarity of the interaction between colloidal particles. Based on this approach, the Coulomb-like interaction between dipole particles in a cholesteric liquid crystal and a crucial change in the character of the interaction in a smectic liquid crystal are predicted.

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.

Effect of collective molecular reorientations on Brownian motion of colloids in nematic liquid crystal.

In the simplest realization of Brownian motion, a colloidal sphere moves randomly in an isotropic fluid; its mean squared displacement (MSD) grows linearly with time τ. Brownian motion in an orientationally ordered fluid--a nematic--is anisotropic, with the MSD being larger along the axis of molecular orientation, called the director. We found that at short time scales, the anisotropic diffusion in a nematic becomes anomalous, with the MSD growing slower or faster than τ; these states are respectively termed subdiffusion and superdiffusion. The anomalous diffusion occurs at time scales that correspond to the relaxation times of director deformations around the sphere. Once the nematic melts, the diffusion becomes normal and isotropic. Our experiment shows that the deformations and fluctuations of long-range orientational order profoundly influence diffusive regimes.

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→∞.

Theory of elastic interaction of colloidal particles in nematic liquid crystals near one wall and in the nematic cell.

We apply the method developed [Chernyshuk and Lev, Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of colloidal elastic interactions between axially symmetric particles in the confined nematic liquid crystal near one wall and in the nematic cell with thickness L. Both cases of homeotropic and planar director orientations are considered. Particularly, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions of the one particle with the wall and within the nematic cell are found as well as corresponding two particle elastic interactions. A set of results has been predicted: The effective power of repulsion between two dipole particles at height h near the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase of dimensionless distance r / h; near the planar wall, the effect of dipole-dipole isotropic attraction is predicted for large distances r > r(dd) = 4.76 h; maps of attraction and repulsion zones are crucially changed for all interactions near the planar wall and in the planar cell; and one dipole particle in the homeotropic nematic cell was found to be shifted by the distance δ(eq) from the center of the cell. The proposed theory fits very well with experimental data for the confinement effect of elastic interaction between spheres in the homeotropic cell [Vilfan et al., Phys. Rev. Lett. 101, 237801 (2008)] in the range 1-1000 kT. The influence of the K(24) and K(13) terms as well as connection with other theoretical approaches are discussed.

Statistical description of Coulomb-like systems.

The solution of the problem of the partition function calculation for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to arbitrary spatially inhomogeneous configurations. Formation of structures in a Coulomb-like system is analyzed and applied to the case of of dusty crystals and two-dimensional colloidal crystals. In the one-dimensional case, an exact solution for the spatial distribution of charged particles is obtained. In the two- dimensional case, the exact partition function for homogeneous distribution of particles is presented. We have analytically derived the necessary condition for the crystal formation in a system of interacting particles in the three-dimensional case.

Elastic interaction between colloidal particles in confined nematic liquid crystals.

The theory of elastic interaction of micrometer-sized axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self-energy of one colloidal particle and interaction energy between two particles in arbitrary confined nematic liquid crystals with strong anchoring condition on the bounding surfaces. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness L are considered and found to be exponentially screened on far distances with decay length lambdadd=L/pi. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that the decay length in quadrupolar interaction is two times smaller than for the dipolar case in the homeotropic cell.

Coexistence of two colloidal crystals at the nematic-liquid-crystal-air interface.

Glycerol droplets at a nematic-liquid-crystal-air interface form two different lattices--hexagonal and dense quasihexagonal--which are separated by the energy barrier and can coexist. Director distortions around each droplet form an elastic dipole. The first order transition between the two lattices is driven by a reduction of the dipole-dipole repulsion through reorientation of these dipoles. The elastic-capillary attraction is essential for the both lattices. The effect has a many-body origin.

Paranematic interaction between nanoparticles of ordinary shape.

We propose a general approach to the description of the long-ranged interaction between nanoparticles (1-10 nm) of ordinary shape in the paranematic phase, i.e., nematic liquid crystal in the isotropic phase. In general case interaction potential is attractive of Yukawa form with derivatives. But it can be anisotropic despite the isotropy of the paranematic phase. The origin of such anisotropy is the shape of nanoparticles. Particular potentials for spherical and cylindrical particles are considered. For the case of nanocylinders anisotropic part of the interaction potential can lead to the orientational ordering of them in the isotropic phase of nematic liquid crystals.

Cluster formation in the system of interacting Bose particles.

Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Bose particles. The condition of cluster formation in both gas and condensed phases was obtained in this system. We studied the dynamics of cluster formation in the limit case of high temperatures. We compared the cluster-formation processes in the attractive system (with short-range interaction) and in the gravitational system at the low temperatures of Bose-Einstein condensate regime.

Ordered droplet structures at the liquid crystal surface and elastic-capillary colloidal interactions.

We demonstrate a variety of ordered patterns, including hexagonal structures and chains, formed by colloidal particles (droplets) at the free surface of a nematic liquid crystal (LC). The surface placement introduces a new type of particle interaction as compared to particles entirely in the LC bulk. Namely, director deformations caused by the particles lead to distortions of the interface and thus to capillary attraction. The elastic-capillary coupling is strong enough to remain relevant even at the micron-scale when its buoyancy-capillary counterpart becomes irrelevant.

Symmetry breaking and interaction of colloidal particles in nematic liquid crystals.

We propose a general approach to the description of the long-ranged elastic interaction in the nematic colloids, based on the symmetry breaking of the director field. The type of the far-field interaction between particles immersed in a nematic host is determined by the way the symmetry is broken in the near-field region around the colloidal particle. This is caused both by the particle's shape and the anchoring at the surface. If the director field near the particle has a set of three symmetry planes, the far-field interaction falls off as d(-5) with d being the distance between particles. If one symmetry plane is absent, a dipolar moment perpendicular to it is allowed and yields dipole-dipole interactions, which decays as d(-3). If both the horizontal and vertical mirror symmetries are broken (it is equivalent to the case when the nonzero torque moment is applied to the particle by the nematic liquid crystal), the particles are shown to attract each other following the Coulomb law. We propose a simple method for the experimental observation of this Coulomb attraction. The behavior of colloid particles in curved director fields is analyzed. Quadrupolar particles with planar anchoring are shown to be attracted toward the regions with high splay deformations, while quadrupoles with homeotropic anchoring are depleted from such regions. When there are many colloidal particles in the nematic solvent, the distortions of the director from all of them are overlapped and lead to the exponential screening in the elastic pair interaction potential. This is a many-body interaction effect. This screening is essential in the real dense colloid systems, such as ferronematics--suspensions of magnetic cylindrical grains in the nematic liquid crystal. External magnetic field induces an elastic Yukawa attraction between them. We apply this attraction to the explanation of the cellular texture in magnetically doped liquid crystals.

Deformation of liquid crystal droplets under the action of an external ac electric field.

Deformation of liquid crystal droplets suspended in liquid polymer matrix under the action of external electric field was observed in dependence of ion concentration in such system. Experimental dependence of droplet elongation vs electric field demonstrates nonmonotonous character with increase of ion concentration. The theory that provides the basic agreement with experimental observation is developed.