Molecular-statistical theory of elasticity in nematic liquid crystals composed of polar and nonpolar molecules.

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant K_{11} which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.

Lasing in liquid crystal systems with a deformed lying helix.

We report on experimental investigations of the lasing effect in novel chiral liquid crystal (CLC) systems with a deformed lying helix (DLH). The lasing is studied for both odd- and even-order field-induced stop-bands, which are characteristic exclusively of the DLH state. The DLH state is achieved in special CLC cells with periodic boundary conditions, when the surface alignment is flipped between planar and vertical states. The alignment surfaces are prepared using focused ion-beam lithography. In an electric field, such CLC systems undergo an orientational transition, when the initial Grandjean-plane texture with the helix axis perpendicular to the CLC layer is transformed into the DLH state with the helix axis oriented in the plane of the layer. Due to field-induced strong deformation, the DLH system is characterized by a set of photonic stop-bands with a fine spectral structure; namely, on these fine-structured sub-bands, we have observed and studied the low-threshold lasing effect.

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers.

Symmetric rod-coil diblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter. It has been found that the tilted lamellar phase appears to be the most stable one at strong segregation. The rod-coil copolymer tilt angle and orientational order parameters have been determined as functions of the segregation strength. The density functional theory of rod-coil diblock copolymers has been generalized to the case of the tilted lamellar phase and used to study the stability of the orthogonal lamellar phase with respect to tilt. The orthogonal phase indeed appears to be unstable in the broad region of the parameter space in the case of relatively strong segregation. It has also been shown that the transition into the tilted lamellar phase is determined by a strong coupling between two independent tilt order parameters.

Molecular theory of liquid-crystal ordering in rod-coil diblock copolymers.

Molecular-statistical theory of rod-coil diblock copolymers is proposed using the general density functional approach which enables one to consider the cases of both weak and strong segregation. The free energy of the system is expressed as a functional of the phase-space densities of rod and coil monomers, which depend on the orientational and translational order parameters. Temperature-concentration phase diagrams are obtained and the profiles of all order parameters are calculated numerically by minimizing the polymer free energy. The lamellar phase is shown to possess strong orientational order which is partially induced by the phase structural anisotropy. The enhanced stability of the lamellar phase is determined by a combination of the microphase separation effects and the emergence of long-range smectic order.

Phase behavior and orientational ordering in block copolymers doped with anisotropic nanoparticles.

A molecular field theory and coarse-grained computer simulations with dissipative particle dynamics have been used to study the spontaneous orientational ordering of anisotropic nanoparticles in the lamellar and hexagonal phases of diblock copolymers and the effect of nanoparticles on the phase behavior of these systems. Both the molecular theory and computer simulations indicate that strongly anisotropic nanoparticles are ordered orientationally mainly in the boundary region between the domains and the nematic order parameter possesses opposite signs in adjacent domains. The orientational order is induced by the boundary and by the interaction between nanoparticles and the monomer units in different domains. In simulations, sufficiently long and strongly selective nanoparticles are ordered also inside the domains. The nematic order parameter and local concentration profiles of nanoparticles have been calculated numerically using the model of a nanoparticle with two interaction centers and also determined using the results of computer simulations. A number of phase diagrams have been obtained which illustrate the effect of nanoparticle selectivity and molar fraction of the stability ranges of various phases. Different morphologies have been identified by analyzing the static structure factor and a phase diagram has been constructed in coordinates' nanoparticle concentration-copolymer composition. Orientational ordering of even a small fraction of nanoparticles may result in a significant increase of the dielectric anisotropy of a polymer nanocomposite, which is important for various applications.

FIB-fabricated complex-shaped 3D chiral photonic silicon nanostructures.

Technologies capable of fabricating complex shaped silicon metasurfaces attract increasing attention. The focused ion beam fabrication technique is considered traditionally as causing thick damaged layers in silicon resulting in a significant rise of the optical absorption loss. We examine the structure of the FIB-fabricated nanostructures on the silicon-on-sapphire (SOS) platform and its optical characteristics before and after thermal oxidation. We show that being thermally oxidised the FIB-patterned silicon subwavelength nanostructure tends to regain its chiral optical features. The impact of the oxidation process on the silicon nanostructure optical behaviour is discussed.

Effect of nanoparticle chain formation on dielectric anisotropy of nematic composites.

A general theory of the dielectric constant of nematic liquid crystal mixtures is presented including the particular case of nematics doped with polar nanoparticles. The results are used to estimate the contribution of chains of polar nanoparticles to the static dielectric anisotropy and birefringence of the nematic composite taking into account contributions from chains of different lengths. The dependence of the dielectric anisotropy on the dipolar interaction strength is considered in detail and it is shown that formation of polar chains of nanoparticles enables one to explain a significant increase of the dielectric constant of the composite as observed experimentally.

Molecular theory of smectic ordering in liquid crystals with nanoscale segregation of different molecular fragments.

A molecular statistical theory of the smectic A phase is developed taking into account specific interactions between different molecular fragments which enables one to describe different microscopic scenario of the transition into the smectic phase. The effects of nanoscale segregation are described using molecular models with different combinations of attractive and repulsive sites. These models have been used to calculate numerically coefficients in the mean filed potential as functions of molecular model parameters and the period of the smectic structure. The same coefficients are calculated also for a conventional smectic with standard Gay-Berne interaction potential which does not promote the segregation. The free energy is minimized numerically to calculate the order parameters of the smectic A phases and to study the nature of the smectic transition in both systems. It has been found that in conventional materials the smectic order can be stabilized only when the orientational order is sufficiently high, In contrast, in materials with nanosegregation the smectic order develops mainly in the form of the orientational-translational wave while the nematic order parameter remains relatively small. Microscopic mechanisms of smectic ordering in both systems are discussed in detail, and the results for smectic order parameters are compared with experimental data for materials of various molecular structure.

Molecular model of biaxial ordering in nematic liquid crystals composed of flat molecules with four mesogenic groups.

Relative stability of uniaxial and biaxial nematic phases is analyzed in a model nematic liquid crystal composed of flat molecules of C2h symmetry with four mesogenic groups rigidly linked to the same center. The generalized effective quadrupole mean-field potential is proposed and its constants are evaluated numerically for the pair intermolecular potential based on Gay-Berne interaction between mesogenic groups. The dependencies of the constants on molecular shape parameters are systematically analyzed. Order parameters of the uniaxial and biaxial nematic phases are evaluated by direct minimization of the free energy at different temperatures. The corresponding phase diagrams are obtained enabling one to study the effects of molecular model parameters on the stability regions of uniaxial and biaxial phases. The results are used to clarify the nature of experimentally observed biaxial ordering in nematic liquid crystals composed of tetrapode molecules with the same symmetry.

Ferroelectric ordering in chiral smectic-C* liquid crystals determined by nonchiral intermolecular interactions.

General microscopic mechanism of ferroelectric ordering in chiral smectic-C* liquid crystals is considered. It is shown that if the mesogenic molecules have a sufficiently low symmetry, the spontaneous polarization is proportional to one of the biaxial vector order parameters of the smectic-C phase. This order parameter may be determined by intermolecular interactions which are not sensitive to molecular chirality. At the same time, the polarization is also proportional to a pseudoscalar parameter which vanishes if the molecules are nonchiral. The general statistical theory of ferroelectric ordering is illustrated by two particular models. The first model is based on electrostatic quadrupole-quadrupole interactions, and it enables one to obtain explicit analytical expressions for the spontaneous polarization. In the second model, the molecular chirality and polarity are determined by a pair of off-center nonparallel dipoles. For this case, the spontaneous polarization is calculated numerically as a function of temperature. The theory provides a more general interpretation of the previous approaches including the classical Boulder model.

Molecular models for ferroelectric liquid crystals with conventional and anomalously weak layer contraction.

A molecular theory of the ferroelectric smectic C* phase has been developed using the simple model of a chiral molecule composed of a uniaxial core and a pair of off-center nonparallel dipoles which determine molecular chirality and polarity. The interaction between uniaxial cores is modeled by a rather general effective potential which can be used to describe smectic materials with both conventional and anomalously weak layer contraction in the smectic C* phase. Spontaneous polarization, tilt, and layer spacing are calculated numerically as functions of temperature, and it is shown that the variation of the polarization generally deviates from that of the tilt angle. It is shown that this deviation is more pronounced in smectic materials tilting with low layer contraction which corresponds to existing experimental data. The model has been used to reproduce qualitatively the experimental data for polarization, tilt and layer spacing for two similar mixtures exhibiting conventional and anomalously weak layer contraction. The polarization and the tilt are also calculated in the case when the smectic A-smectic C* transition is characterized by the biaxial primary order parameter.

Molecular theory of layer contraction in smectic liquid crystals.

The period of the layered structure in smectic A and smectic C liquid crystal phases has been calculated numerically by direct minimization of the mean-field free energy which takes into account the interaction between molecules in adjacent smectic layers. The smectic layer spacing is calculated for two systems characterized by conventional and anomalously weak layer contraction in the smectic C phase. It is then compared with the simple estimate based on the average projection of the molecular long axis on the smectic layer normal. For both systems, temperature variation of the average molecular projection is qualitatively similar to that of the calculated layer spacing although certain quantitative deviations exist.

Molecular model for de Vries type smectic- A -smectic- C phase transition in liquid crystals.

We develop both phenomenological and molecular-statistical theory of smectic- A -smectic- C phase transition with anomalously weak smectic layer contraction. Using a general mean-field molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition both in conventional and de Vries type smectics. The theoretical results are in excellent agreement with experimental data. The approach can be used to describe tilting transitions in other soft matter systems.

Order-disorder molecular model of the smectic-A-smectic-C phase transition in materials with conventional and anomalously weak layer contraction.

We develop a molecular-statistical theory of the smectic-A-smectic-C transition which is described as a transition of the order-disorder type. The theory is based on a general expansion of the effective interaction potential and employs a complete set of orientational order parameters. All the order parameters of the smectic-C phase including the tilt angle are calculated numerically as functions of temperature for a number of systems which correspond to different transition scenario. The effective interaction potential and the parameters of the transition are also calculated for specific molecular models based on electrostatic and induction interaction between molecular dipoles. The theory successfully reproduces the main properties of both conventional and so-called "de Vries-type" smectic liquid crystals, clarifies the origin of the anomalously weak layer contraction and describes the tricritical behavior at the smectic-A-smectic-C transition. The "de Vries behavior," i.e., anomalously weak layer contraction is also obtained for a particular molecular model based on interaction between longitudinal molecular dipoles. A simple phenomenological model is presented enabling one to obtain explicit expressions for the layer spacing and the tilt angle which are used to fit the experimental data for a number of materials.

Theory of critical enhancement of photorefractive beam coupling.

We develop the idea of critical enhancement of the photorefractive response near the threshold of parametric excitation of space-charge waves (the spatial subharmonics) taking into account the vectorial character of beam coupling and a fairly strong broadening of the nonlinear resonance owing to light absorption. The results of our calculations are a description of the measurable characteristics of critical enhancement and optimization of the experimental conditions for detection of anomalously high amplification gain factors in cubic Bi(12)SiO(20) crystals.