Properties of the nematic–isotropic phase transition in polymer and low molecular weight liquid crystals doped with nanoparticles have been studied both experimentally and theoretically in terms of molecular mean-field theory. The variation of the transition temperature and the transition heat with the increasing volume fraction of CdSe quantum dot nanoparticles in copolymer and low molecular weight nematics has been investigated experimentally and the data are interpreted using the results of the molecular theory which accounts for a possibility of phase separation when the system undergoes the nematic–isotropic transition. The theory predicts that the nematic and isotropic phases with different concentrations of nanoparticles may coexist over a broad temperature range, but only if the nanoparticle volume fraction exceeds a certain threshold value which depends on the material parameters. Such unusual phase separation effects are determined by the strong interaction between nanoparticles and mesogenic groups and between nanoparticles themselves.

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.

A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole-dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole-dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole-dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.

The qualitative microscopic mechanism of ferroelectric ordering in smectic C* liquid crystals originally proposed by de Gennes and others is analysed in detail using the molecular-statistical approach. The general expression is obtained for the spontaneous polarisation of the smectic C* phase composed of chiral and polar molecules of the C 2 symmetry. The polarisation is shown to be determined by molecular chirality, molecular transverse dipole and the non-polar biaxial order parameter which does not vanish in the non-chiral smectic C phase. A particular molecular model is considered in which molecular chirality and molecular biaxiality are determined by the pair of off-centre transverse molecular dipoles. In the context of this model the spontaneous polarisation is evaluated both analytically and numerically.

Order parameters and phenomenological theory for both high- and low-symmetry biaxial nematic phases are presented and it is predicted that the chiral low-symmetry biaxial phase must be ferroelectric. This conclusion is based on general symmetry arguments and on the results of the Landau-de Gennes theory. The microscopic mechanism of the ferroelectric ordering in this chiral biaxial phase is illustrated using a simple molecular model based on dispersion interactions between biaxial molecules of low symmetry. Similar to the chiral smectic C* phase, the ferroelectricity in the chiral biaxial nematic phase is improper, i.e., polarization is not a primary order parameter and is not determined by dipolar interactions. Ferroelectric ordering in biaxial nematics may be found, in principle, in materials composed of chiral analogues of the tetrapod molecules which are known to exhibit biaxial phases.