Anchoring-induced nonmonotonic velocity versus temperature dependence of motile bacteria in a lyotropic nematic liquid crystal.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible.

Analytical canonical partition function of a quasi-one-dimensional system of hard disks.

The exact canonical partition function of a hard disk system in a narrow quasi-one-dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result, the many body problem is reduced to solving the single transcendental equation. The pressures along and across the pore, distributions of contact distances along the pore, and disks' transverse coordinates are found analytically and presented in the whole density range for three different pore widths.

Interaction of supramolecular aggregates and the enhanced optical torque on the director in a dye doped nematic liquid crystal.

There has been strong experimental evidence that molecules of some dyes in an anisotropic solvent, nematic liquid crystal, form aggregates. We present a detailed experimental analysis of the light-induced director reorientation (DR) in a dye-doped nematic liquid crystal (known as the Jánossy effect) and a theoretical model of its strong enhancement based on the aggregates' interaction. The DR transition is found to be very different from the Frederiks effect.

Controlled Multistep Self-Assembling of Colloidal Droplets at a Nematic Liquid Crystal-Air Interface.

We present a controlled cascade of self-assemblings of colloidal droplets at a nematic liquid crystal-air interface into large-scale ordered structures. Changing the tilt of the droplet-induced elastic dipoles via its dependence on the nematic film thickness, we are able to control the dipole-dipole interaction and thus the self-assembling regime. For a progressively large tilt, droplets form anisotropic lattices, which then transform into arrays of repulsive chains, then to bands of half-period-shifted densely bound chains.

Statistical model of a flexible inextensible polymer chain: The effect of kinetic energy.

Because of the holonomic constraints, the kinetic energy contribution in the partition function of an inextensible polymer chain is difficult to find, and it has been systematically ignored. We present the first thermodynamic calculation incorporating the kinetic energy of an inextensible polymer chain with the bending energy. To explore the effect of the translation-rotation degrees of freedom, we propose and solve a statistical model of a fully flexible chain of N+1 linked beads which, in the limit of smooth bending, is equivalent to the well-known wormlike chain model.

Elastic multipoles in the field of the nematic director distortions.

Theory of the interaction between all types of elastic dipoles and quadrupoles and distortions of the nematic director is presented. If a particle is small relative to the characteristic distortion length, the interaction is determined by the director derivatives at the particle location. We consider a spherical particle since, even under the standard assumptions of the multipole theory (weak deformations, one constant approximation), the problem can be solved analytically only in this case.

Active shape-morphing elastomeric colloids in short-pitch cholesteric liquid crystals.

Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well as locomotion in the case of a nonreciprocal shape morphing.

Stability and minimum size of colloidal clusters on a liquid-air interface.

A vertical force applied to each of two colloids, trapped at a liquid-air interface, induces their logarithmic pairwise attraction. I recently showed [Phys. Rev.

Chiral dipole induced by azimuthal anchoring on the surface of a planar elastic quadrupole.

A spherical colloid with the tangential surface nematic director, aligned along the surface meridians, is known as a planar elastic quadrupole. The azimuthal anchoring, however, can induce a deviation of the planar director from the meridional lines. We show that a helical component of the planar surface director at the spherical surface of a planar quadrupole removes all the reflection symmetry planes and gives rise to a chiral elastic dipolar component.

Dipolar colloids in nematostatics: tensorial structure, symmetry, different types, and their interaction.

In spite of the analogy to the electrostatics, the three-dimensional colloidal nematostatics is substantially different in both its mathematical structure and its physical implications. The general tensorial structure of elastic multipoles derived in V. M.

Colloid-wall interaction in a nematic liquid crystal: the mirror-image method of colloidal nematostatics.

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M.

Strong collective attraction in colloidal clusters on a liquid-air interface.

It is shown that in a cluster of many colloids, trapped at a liquid-air interface, the well-known vertical-force-induced pairwise logarithmic attraction changes to a strongly enhanced power-law attraction. In large two-dimensional clusters, the attraction energy scales as the inverse square of the distance between colloids. The enhancement is given by the ratio eta = (square of the capillary length) / (interface surface area per colloid) and can be as large as 10;{5} .

Stripe domains in a nearly homeotropic nematic liquid crystal: a bend escaped state at a nematic-smectic-A transition.

We report an observation and mechanism of spontaneous periodic modulations of the nematic director close to the temperature T(NA) of a nematic-to-smectic-A phase transition if the surface alignment slightly differs from a pure homeotropic one. Stripe domains appear in the nematic phase about one degree above T(NA) and persist into the Sm A phase. The instability of the homogeneous state with respect to stripe domains is shown to be related to a very large bend constant which is much larger than the twist and splay elastic constants.

Coulomb-like interaction in nematic emulsions induced by external torques exerted on the colloids.

An external mechanical torque on colloids immersed in a nematic liquid crystal can induce a Coulomb-like 1/r interaction between them [Lev and Tomchuk, Phys. Rev. E 59, 591 (1999); Lev, ibid.

Elastic charge density representation of the interaction via the nematic director field.

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies.

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.

Full energy expression of a uniaxial nematic phase with spatially dependent density and order parameters: From microscopic to macroscopic theory.

We present a microscopic derivation of the full macroscopic energy expression of a spatially bounded uniaxial nematic phase. The surface is described by spatial variations of the density and scalar order parameters of all even orders. The method developed in the paper allowed us to unambiguously separate the surface elastic K24 and K13 terms and isotropic and anisotropic surface tension (anchoring).

Intermediate periodic "saddle-splay" nematic phase in the vicinity of a nematic-smectic-A transition.

We consider possible spontaneous modulations of the nematic director induced by the elastic saddle-splay K24 term when the value of the elastic constant K24 does not satisfy the Ericksen stability condition for the homogeneous ground state. According to the standard formula expressing K24 in terms of the twist elastic constant K22, this can be expected close to the nematic-smectic-A transition where K22 becomes very large. It is predicted that in a planar nematic layer (or, more generally, if the surface director alignment is sufficiently close to a planar one), a modulated phase with observable long wavelength period can occur in samples considerably thicker than the anchoring extrapolation length.

Non-Debye screening of a surface charge and a bulk-ion-controlled anchoring transition in a nematic liquid crystal.

We study the anchoring mechanism due to substrate-adsorbed ions by examining a related anchoring transition. An analytical solution to the Poisson equation shows that, as their number suffices for a non-negligible anchoring contribution, the surface field is screened over some characteristic microscopic distance. It is shown both theoretically and experimentally that the critical temperature of the transition can be controlled by bulk ion density through its relation to the density of adsorbed ions.

Spontaneous deformations of the uniform director ground state induced by the surfacelike elastic terms in a thin planar nematic layer.

We study the effect of the divergence (surfacelike) K24 and K13 terms on stability of the uniform ground state of a nematic phase. It is shown that the K13 term can effectively boost the action of the K24 term. As a result, even if the two Ericksen stability conditions are satisfied, spontaneous deformations can occur in geometries with a sufficiently small volume-to-surface ratio.