Molecular models for the smectic A–smectic C phase transition in a system of biaxial molecules

A molecular theory of the smectic A-smectic C transition in a system of biaxial molecules is developed in the mean-field approximation. The influence of molecular biaxiality on the transition is considered in detail and it is demonstrated how the biaxial order parameters are induced by the tilt. It is shown that the ordering of biaxial molecules of low symmetry in the smectic C phase is generally described by ten independent orientational order parameters, and there exist three different tilt angles which specify the tilt of three ordering tensors. The order parameters are calculated numerically as functions of temperature for two models of biaxial molecules: molecules with two principal axes and molecules with a pair of off-center transverse dipoles. A substantial difference between the three tilt angles is found, which makes impossible a strict definition of a unique director in the smectic C phase. It is also shown that biaxial interactions may lead to an anomalously weak layer contraction in the smectic C phase. Finally, it is demonstrated that the smectic A-smectic C phase transition may be directly driven by biaxial intermolecular interactions. In this case, the tilt of long molecular axes is not a primary order parameter, and its temperature dependence is very different from convention

On the measurement of the orientational order parameters in biaxial liquid crystals using the polarised infrared technique

The limits of the applicability of the Polarised Infrared (Fourier transform infrared) spectroscopy technique, which is used to measure the order parameters of biaxial liquid crystals, is investigated in detail for different experimental geometries and cell thicknesses. General expressions for the transmittance of the polarised infrared radiation by a biaxial liquid crystal material in planar and homeotropic cells are obtained in the general case of oblique incidence. These expressions are then simplified in the limiting cases of thin and thick cells, and in both cases the relationship is established between the cell transmittance and the components of the imaginary part of the infrared molecular permittivity. It is shown that simple expressions, used in the literature to extract the values of the biaxial order parameters, are valid only for thin cells and in specific geometries when light propagates along one of the optical axes of the material. For thicker cells typical for experimental conditions, approximate expressions are obtained which are to be used to reveal the order parameters of biaxial liquid crystals. Various types of experimental geometries are discussed including those suitable for measurements of the order parameters, and those to be avoide

Model-independent structure and resonant X-ray spectra of intermediate smectic phases

It is shown that the orientational structure of intermediate smectic phases can be determined using the symmetry properties of the general free energy with arbitrary orientational coupling between smectic layers, without addressing a particular model. The structure of three- and four-layer intermediate phases, obtained in this way, corresponds to experimental data. The same method enables one to predict the structure of intermediate phases with periodicity of five and six layers, which have not been observed experimentally so far. The resonant X-ray spectra of the five- and six-layer intermediate phases with predicted structure have also been calculated. These spectra are characterized by a number of features which enable one to distinguish five-layer and six-layer intermediate phases from phases with smaller periods

Mean-field theory of a nematic liquid crystal doped with anisotropic nanoparticles

In the framework of molecular mean-field theory we study the effect of nanoparticles embedded in nematic liquid crystals on the orientational ordering and nematic–isotropic phase transition. We show that spherically isotropic nanoparticles effectively dilute the liquid crystal medium and decrease the nematic–isotropic transition temperature. At the same time, anisotropic nanoparticles become aligned by the nematic host and, reciprocally, improve the liquid crystal alignment. The theory clarifies the microscopic origin of the experimentally observed shift of the isotropic–nematic phase transition and an improvement of the nematic order in composite materials. A considerable softening of the first order nematic–isotropic transition caused by strongly anisotropic nanoparticles is also predicted

Theory of extraordinary light transmission through arrays of subwavelength slits

We propose a self-consistent theory of the extraordinary light transmission through periodic arrays of subwavelength holes in metals. Its basis is an expansion of the light fields in terms of exact eigenmodes- propagating, evanescent, and anomalous-investigated in our recent paper and matching at the interfaces using the exact boundary conditions. An excellent convergence of this expansion has allowed us to decompose the anomalous transmission phenomenon into elementary parts and to investigate the characteristic parametric dependences. Transmission properties of a single interface play a key role in our theory in the subwavelength range. They include the coefficient of energy transmission into the propagating mode and the phases of the reflected and transmitted waves. These key parameters possess remarkable resonant dependences on the wavelength of light; they are sensitive to the size of the holes and rather insensitive to weak losses. The surfaceplasmon- related features of the above characteristics are established. Transmission properties of a slab are expressed by the single-interface parameters, the phase incursion for the propagating mode, and the propagating losses

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

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