Ordering of ferromagnetic nanoparticles in nematic liquid crystals.

Dispersions of magnetic nanoparticles in a nematic liquid crystal were investigated as magnetic fields were applied in three different boundary condition geometries: (i) planar substrates and B⊥n, (ii) planar substrates and B‖n, and (iii) homeotropic substrates and B⊥n. Particle chaining is observed when a magnetic field is applied, with a periodicity perpendicular to the chains. Furthermore, linear chains are observed for the magnetic field applied perpendicular to the director, while zigzag chains are formed when the magnetic field direction is parallel to the director field. This is attributed to a change from a dipolar defect configuration around dispersed nanoparticles, to a quadrupolar one, i.e. the change from satellite to Saturn-ring defects. This effect is largely independent of the sample thickness. The dynamic development of the chain length, as well as their two-dimensional order parameter was studied in all cases. Chain lengths increased rapidly until saturation at approximately l = 30 µm after a time of about t = 10 s. Similarly, the chain order parameters increased until saturation between S = 0.8-0.9, independent of sample geometry.

Dispersions of multi-wall carbon nanotubes in ferroelectric liquid crystals.

The electro-optic and dielectric properties of ferroelectric liquid crystal-multi-wall carbon nanotube dispersions were investigated with respect to temperature and nanotube concentration. The main physical properties, such as tilt angle, spontaneous polarization, response time, viscosity, and Goldstone-mode relaxation strength and frequency were studied. While all dispersions exhibit the expected temperature dependencies of their physical properties, their dependence on nanotube concentration is still a controversial discussion in literature, with several contradicting reports. For increasing nanotube concentration we observed a decrease in tilt angle, but an increase in spontaneous polarisation, the latter explaining the enhancement of the bilinear coupling coefficient, and the dielectric relaxation strength. Despite the increase in polarization, the electro-optic response times slow down, which suggests an increase of rotational viscosity along the tilt cone. It is anticipated that the latter also accounts for the observed decrease of the Goldstone-mode relaxation frequency for increasing nanotube concentration.

Circular polarization interferometry: circularly polarized modes of cholesteric liquid crystals.

We describe a novel polarization interferometer which permits the determination of the refractive indices for circularly-polarized light. It is based on a Jamin-Lebedeff interferometer, modified with waveplates, and permits us to experimentally determine the refractive indices nL and nR of the respectively left- and right-circularly polarized modes in a cholesteric liquid crystal. Whereas optical rotation measurements only determine the circular birefringence, i.e. the difference (nL - nR), the interferometer also permits the determination of their absolute values. We report refractive indices of a cholesteric liquid crystal in the region of selective (Bragg) reflection as a function of temperature.

Orientational order parameters of a de Vries-type ferroelectric liquid crystal obtained by polarized Raman spectroscopy and x-ray diffraction.

The orientational order parameters (P{2}) and (P{4}) of the ferroelectric, de Vries-type liquid crystal 9HL have been determined in the SmA and SmC phases by means of polarized Raman spectroscopy, and in the SmA phase using x-ray diffraction. Quantum density functional theory predicts Raman spectra for 9HL that are in good agreement with the observations and indicates that the strong Raman band probed in the experiment corresponds to the uniaxial, coupled vibration of the three phenyl rings along the molecular long axis. The magnitudes of the orientational order parameters obtained in the Raman and x-ray experiments differ dramatically from each other, a discrepancy that is resolved by considering that the two techniques probe the orientational distributions of different molecular axes. We have developed a systematic procedure in which we calculate the angle between these axes and rescale the orientational order parameters obtained from x-ray scattering with results that are then in good agreement with the Raman data. At least in the case of 9HL, the results obtained by both techniques support a "sugar loaf" orientational distribution in the SmA phase with no qualitative difference to conventional smectics A. The role of individual molecular fragments in promoting de Vries-type behavior is considered.

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 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.

Frustration between syn- and anticlinicity in mixtures of chiral and non-chiral tilted smectic-C-type liquid crystals.

We study the effects of mixing ferroelectric and antiferroelectric liquid-crystal compounds (FLCs and AFLCs) when the former are strictly synclinic and the latter strictly anticlinic, i.e. one mixture component exhibits only SmC* and the other only SmC(a)* as tilted phase. Three different paths between syn- and anticlinicity were detected: transition directly between SmC* and SmC(a)*, transition via the SmC(beta)* and SmC(gamma)* subphases, or by "escaping" the clinicity frustration by reducing the tilt to zero, i.e. the SmA* phase is extended downwards in temperature, separating SmC* from SmC(a)* in the phase diagram. The most common path is the one via the subphases, demonstrating that these phases appear as a result of frustration between syn- and anticlinic and, consequently, between syn- and antipolar order. For assessing the role of chirality, we also replaced the FLC with non-chiral synclinics. With one of the AFLCs, the route via supbhases was detected even in this case, suggesting that chirality--although necessary--does not have quite the importance that has previously been attributed to the appearance of the subphases. The path chosen in the mixture study seemed to be determined mainly by the synclinic component, the subphase induction occurring only when the SmA*-SmC* transition was second order.

Smectic-A*-smectic-C* transition in a ferroelectric liquid crystal without smectic layer shrinkage.

The smectic layer spacing of a nonfluorinated ferroelectric liquid crystal (FLC) compound with almost no shrinkage and only minor tendency to form zigzag defects was characterized by small angle x-ray diffraction. The material lacks a nematic phase. The smectic-A*-smectic-C* phase transition was studied by measuring the thermal and electric field response of the optical tilt and the electric polarization. These properties are described very well by a Landau expansion even without introduction of a higher-order Theta(6) term. This result suggests a pure second-order phase transition far from tricriticality and differs considerably from the typical behavior of the A*-C* transition in most FLC materials.