Theoretical model for layer reorientation in smectic A* liquid crystals subject to an oblique magnetic field

Recently, Carlsson and Osipov reported on observations of the rotation of smectic layers under certain experimental conditions, and a dynamic theory describing such rotations was presented [Carlsson, T., and Osipov, M. A., 1999, Phys. Rev. E, 60, 5619]. In the present work, the rotational motion of the smectic layers of a SmA* liquid crystal, over which an oblique magnetic field has been applied, is studied theoretically by the aid of this theory. The role of the interaction between the smectic layers and the substrates is discussed and it is shown that if this interaction is small enough, the smectic layers orient themselves in such a way that the layer normal is almost parallel to the magnetic field. The relevant material parameters governing the dynamical response of the induced tilt and the layer normal are identified, and the time dependence of the response of these two dynamical variables is calculated. From this calculation, expressions for the response times of the system are given and a numerical value of the rotational viscosity of the smectic layers is estimated.     

Dynamics of the smectic layer reorientation of ferroelectric liquid crystals

Detailed experimental results of a systematic investigation of the dynamics of the in-plane smectic layer reorientation in SmC* ferroelectric liquid crystals on application of different types of asymmetric electric fields are reported. The reversible reorientation of smectic layers is characterized as a function of field asymmetry, electric field amplitude, frequency, cell gap and temperature. On the basis of the observed behaviour we discuss a phenomenological interpretation of the smectic layer reorientation in terms of dominant influences director switching, convection due to ionic motion and liquid crystal substrate interactions which limit the rotation to the amount of twice the tilt angle.     

Horizontal chevron domain formation and smectic layer reorientation in SmC* liquid crystals stabilized by polymer networks

The influence of a polymer network, stabilizing an initial texture of horizontal chevron geometry, on the in-plane smectic C* layer reorientation process is studied for different applied electric field conditions. As expected, the reorientation of smectic layers is strongly slowed down and eventually suppressed by the network, even at rather low monomer concentrations. Polymer network formation in a uniformly reoriented smectic layer state reveals that the network acts in two ways: first it gives a biased elastic torque counteracting a field of such symmetry as to cause a change from the templated layer direction; second it introduces an increased effective viscosity counteracting the reorientation in both directions. The behaviour of samples stabilized by two different kinds of polymer networks, created in between the smectic layers (intra-layer) and across them (inter-layer), is then investigated and discussed.     

Horizontal chevron domain formation and smectic layer reorientation in SmC* liquid crystals stabilized by polymer networks

The influence of a polymer network, stabilizing an initial texture of horizontal chevron geometry, on the in-plane smectic C* layer reorientation process is studied for different applied electric field conditions. As expected, the reorientation of smectic layers is strongly slowed down and eventually suppressed by the network, even at rather low monomer concentrations. Polymer network formation in a uniformly reoriented smectic layer state reveals that the network acts in two ways: first it gives a biased elastic torque counteracting a field of such symmetry as to cause a change from the templated layer direction; second it introduces an increased effective viscosity counteracting the reorientation in both directions. The behaviour of samples stabilized by two different kinds of polymer networks, created in between the smectic layers (intra-layer) and across them (inter-layer), is then investigated and discussed.     

Optical observations of layer ordering in helial smectic A* liquid crystals

We report the first optical microscopic observation of characteristic textures and the associated layer ordering in a recently discovered, helical smectic A* phase on a multiple domain substrate. The experimental results are quite unusual but consistent with a mean-field model of the twisted grain boundary phase.     

Nature of smectic A*-C* phase transitions in a series of ferroelectric liquid crystals with little smectic layer shrinkage

The smectic layer spacing of two homologous series of ferroelectric liquid crystal compounds was characterized by small-angle x-ray diffraction and different degrees of smectic layer shrinkage on cooling from the SmA* into the SmC* phase were observed. The smectic A*-smectic C* phase transition was further studied by measuring the thermal and electric field effects on the optical tilt angle and the electric polarization. With decreasing length of the alkyl terminal chain the phase transition changes from tricritical exhibiting high layer shrinkage to a pure second-order transition with almost no layer shrinkage. This is explained by the increased one-dimensional translational order of the smectic layers, which seems to promote the "de Vries"-type [Mol. Cryst. Liq. Cryst. 41, 27 (1977)] smectic A*-C* phase transition with no or little layer shrinkage.     

Shear flow and magnetic field effects on smectic C,C*, CM and C*M liquid crystals

Abstract

The continuum equations of Leslie et al. [1] for smectic C, and the extension of this theory for chiral smectic C* [2], are applied to problems involving simple planar layer configurations which accommodate uniform layer thickness constraints. The chiral smectic C*_M and non-chiral smectic C_M [3] are considered as either biaxial smectic A phases or antiferroelectric smectic C phases and are therefore included as interesting degenerate cases of the smectic C* and C phases, respectively. The effects of static and time dependent magnetic fields on these materials are compared with related deformations occurring in nematics [4] and cholesterics [5,6]. Their reaction to applied shears is also investigated yielding examples of flow alignment, induced secondary flows and unwinding of the chiral helix and testing the validity of enforcing a constant layer thickness.     

Ferroelectric polysiloxane liquid crystals with 'de Vries'-type smectic A*-smectic C* transitions

We report preliminary results of optical and small angle X-ray scattering (SAXS) experiments on the smectic A*-smectic C* transition in two ferroelectric liquid crystalline polysiloxanes. Although the optical tilt angle in the SmC* phases reaches values up to 30°, temperature-dependent SAXS measurements clearly reveal that the smectic layer spacing is basically conserved during the A*-C* transition as well as in the subsequent C* phase. Connected with the A*-C* transition we further observed a significant increase in birefringence, hence reflecting an increase of orientational order. The practical absence of layer shrinkage and the enhanced orientational ordering are consistent with the de Vries diffuse cone model of smectic A-smectic C transitions.     

Layer distortions induced by a magnetic field in planar samples of smectic C liquid crystals

This article derives theoretical results for the onset of the Helfrich-Hurault transition in smectic C liquid crystals induced by a magnetic field applied parallel to the smectic layers. A suitable quadratic energy in terms of the smectic layer displacement u is derived from the nonlinear version of the smectic C energy. This energy is minimized via averaging to enable the calculation of a critical field strength H _c for the onset of layer distortions. Comparisons are made with known results for the corresponding geometry in the smectic A case. An estimate for the value of the smectic C elastic constant A ₁₂ can also be made by considering characteristic length scales.     

Layer distortions induced by a magnetic field in planar samples of smectic C liquid crystals

This article derives theoretical results for the onset of the Helfrich-Hurault transition in smectic C liquid crystals induced by a magnetic field applied parallel to the smectic layers. A suitable quadratic energy in terms of the smectic layer displacement u is derived from the nonlinear version of the smectic C energy. This energy is minimized via averaging to enable the calculation of a critical field strength H_c for the onset of layer distortions. Comparisons are made with known results for the corresponding geometry in the smectic A case. An estimate for the value of the smectic C elastic constant A₁₂ can also be made by considering characteristic length scales.     

Ferromagnetic liquid crystals for magnetic field visualisation

In this paper, we demonstrate how to apply recently discovered ferromagnetic nematic liquid crystal for visualisation of magnetic fields. The material exhibits strong optical response to both external electric and magnetic fields, which gives us an opportunity to use it for the detection of an area of magnetic vector field in a way that both, the magnitude and the direction of a given field can be simultaneously measured. We discuss the physical model that describes the behaviour of ferromagnetic liquid crystal placed in a liquid crystal cell and demonstrate the method of extracting the information about an arbitrary magnetic field from the combination of magneto-optic and electro-optic response of the sample placed in that field. We have applied the principle to a special case, where magnetic field was visualised on a 2D area near a cylindrical permanent magnet.     

A backflow effect in smectic C liquid crystals

This paper discusses the influence upon a smectic C liquid crystal cell of backflow induced by the relaxation of alignment following the removal of a strong electric or magnetic field. Our study, based upon a recently proposed continuum theory, concentrates upon the homeotropic configuration in which the smectic layers are parallel to the boundary plates, but some consideration is also given to the bookshelf geometry. Although the governing equations prove to be rather complex, some progress is possible analytically by repeating an approximation made in the corresponding problem for a nematic.     

Point-like impurity-dislocation interactions in smectic A liquid crystals

The displacement field created in the neighbourhood of a point-like impurity, its self-energy and point-like impurity-dislocation interaction are calculated for a smectic A liquid crystal in the approximation of small deformations. The binding energy of a point defect to an edge dislocation is also estimated. The use of the Peach-Kochler formula as a basis for the calculation of the dislocation interaction with other defects is discussed.     

Point-like impurity-dislocation interactions in smectic A liquid crystals

Abstract

The displacement field created in the neighbourhood of a point-like impurity, its self-energy and point-like impurity-dislocation interaction are calculated for a smectic A liquid crystal in the approximation of small deformations. The binding energy of a point defect to an edge dislocation is also estimated. The use of the Peach-Kochler formula as a basis for the calculation of the dislocation interaction with other defects is discussed.     

Stimulated light scattering in smectic A liquid crystals

The non-linear interaction of arbitrary polarized light with smectic layer deformations in smectic A liquids (S_A) is considered. It is shown that the combined effect of anisotropy, fluidity and a characteristic kind of deformation cause a number of specific non-linear optical phenomena. Two-wave mixing in S_A transforms into a partly degenerate four-wave mixing (FWM) when the polarization and the direction of propagation of the coupled electromagnetic (EM) waves are arbitrary. The interference of the EM waves gives rise to a dynamic grating of layer deformations without a change of mass density of S_A. In the resonant case a propagating mode of a second sound (SS) is excited. The non-linear phenomena are analysed by solving the self-consistent system of the Maxwell equations for the non-linear anisotropic inhomogeneous medium and the hydrodynamic equations of S_A in the external EM field. The explicit expressions of the EM and SS waves amplitudes are obtained. It is shown that the coupled fundamental EM waves undergo the parametric amplification and the phase cross-modulation, and their amplitudes as well as the SS wave amplitude are spatially localized. The energy transfer between the coupled EM waves is non-reciprocal. The scattering of the fundamental EM waves by the dynamic grating results in the appearance of additional harmonics with combination frequencies and wavevectors. The light induced dynamic grating also generates a longitudinal electric field due to the flexoelectric effect.     

Critical behaviour of nematic liquid crystals in oblique magnetic fields

The static critical behaviour of a bulk nematic liquid crystal sample in an oblique magnetic field is analysed. When a magnetic field is applied at a suitable angle alpha with respect to the initially homogeneous nematic director, a spatially inhomogeneous director pattern can be formed. The transition to the deformed state and the formation of walls between the domains resulting from the two equally stable configurations above the transition are studied. The width of the walls is found to diverge at the transition. The critical exponents corresponding to the transition and wall formation are shown to be characteristic of a mean field second order phase transition.     

Energetics of screw dislocations in smectic A liquid crystals

We derive the self-energy of a single screw dislocation in smectic A liquid crystals allowing for bend curvature in the bulk. For the core region two models are investigated: a nematic one including bend and twist curvature and an isotropic one including surface curvature energy. The former is energetically favourable. For both models the interaction force between two parallel screw dislocations is zero within the linear theory. Taking into account non-linearities perturbatively, an interaction potential is obtained, which is proportional to the logarithm of the distance of the screw dislocations.     

Preliminary communication Dispersion of the optical axes in smectic C* liquid crystals

Optical axes dispersion denotes the dependence of the orientation of the indicatrix and the optical axes on the wavelength of light. Theory predicts optical axes dispersion in optically biaxial phases with low crystallographic symmetry, like the C 2h-symmetry of SmC or the C2 symmetry of SmC* phases. The magnitude of this axes dispersion was measured electrooptically for two liquid crystal materials exhibiting SmC* phases using several wavelengths of light. Far below the phase transition temperature, the wavelength dispersion of the optical tilt is about 1-2 (5-10% of the total tilt) over the range of visible wavelengths.