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1.
DIFFRACTION GRATINGS FORMED BY BENT-CORE LIQUID CRYSTALS IN THE TWIST – BEND NEMATIC PHASE
Muhammad Ali, 2021, doctoral dissertation

Abstract: In this thesis, we study the structure and optical transmission properties of the twist-bend nematic liquid crystalline phase, made of bent dimers, confined in thin planar cells. Confinement leads to the formation of a periodic modulated structure, the formation of which is explained as follows. The twist-bend nematic phase is characterized by a heliconical modulation of the molecular long axes. Due to a short pitch of modulation (approximately 10 nm), the twist-bend nematic phase behaves as a pseudo-layered medium. At temperatures below the nematic – twist-bend nematic phase transition, the heliconical pitch and thus the thickness of the pseudo-layers reduces, which leads to a two-dimensional undulation of pseudo-layers in the direction perpendicular to the cell surfaces and along the surfaces. The undulated structure is responsible for a stripe texture observed under a polarizing microscope and acts as a diffraction grating. We constructed theoretical models to predict the pseudo-layer structure of a confined twist-bend nematic phase and to describe the properties of light diffracted on such cells. The free energy of the two-dimensional pseudo-layer structure of the twist-bend nematic phase is expressed in terms of the nematic director field, by which we describe the direction of the heliconical axis, and a complex smectic order parameter, the gradient of which gives the direction of the layer normal. At first, we assume that pseudo-layers are perpendicular to the surfaces (bookshelf geometry) and find a stable structure by assuming an ansatz for the pseudo-layer displacement from the bookshelf geometry and then minimizing the free energy at a very strong and very weak surface anchoring. In this way a threshold condition for the onset of the modulated structure is obtained, as well as the amplitude and period of modulation. Next, we assume that, at the onset of the twist-bend nematic phase, pseudo-layers are formed at some angle (pre-tilt) with respect to the surface. We find that in both cases, the bookshelf and pre-tilted one, the calculated period of modulation far from the phase transition is always approximately twice the cell thickness, which agrees with experimental observations. The properties of light diffracted by the spontaneously formed grating were studied both experimentally and theoretically. We measured the intensity and polarization properties of the first two orders of the diffracted light and the temperature dependence of the polarization of the second order diffraction peaks. To predict the observed properties of the diffracted light and to simplify the description of such gratings, we consider different preliminary models of a one-dimensional spatial variation of the optic axis, the direction of which is given by two angles. A transfer matrix method is used and a good agreement between the experimental and theoretical results is obtained. In a more comprehensive approach, we determine the spatial variation of the optic axis direction from the modeled structure. The electric field in the diffracted light is obtained by using the transfer matrix method and beam propagation method. In the case of a pre-tilt of the pseudo-layers and very strong surface anchoring both methods give good qualitative agreement with experimental results, only in the case of the temperature dependence of the second order diffraction peaks, a more complex beam propagation method is superior to the transfer matrix method. The thesis is divided into three parts. In the first part, we focus on the physical properties of the twist-bend nematic phase and its structure in thin planar cells. In the second part, a continuum model is proposed and finally, the properties of diffracted light are discussed and theoretically predicted by using the beam propagation method and transfer matrix method.
Keywords: Bent-dimer liquid crystals, twist-bend nematic phase, undulation of pseudo-layers, polarization, diffraction grating, beam propagation method, transfer matrix method.
Published in DKUM: 21.10.2021; Views: 599; Downloads: 57
.pdf Full text (10,65 MB)

2.
Ferroelectric smectic-A phase made of bent-core liquid crystals: Structure and Dielectric response in thin cells
Kristina Leskovar, 2016, doctoral dissertation

Abstract: In the thesis we study the structure and response of bent-core liquid crystals in the orthogonal ferroelectric Smectic-A (SmAP$_F$) phase in thin planar cells. We construct a phenomenological continuum model to study the structure in thin planar cells. A set of molecules within a small volume is presented by the director ($vec{n}$), which defines the average direction of the long molecular axes within this volume, and by the polar director ($vec{p}$), which points in the direction of local polarization. We choose a geometry in which the director in the smectic layer is constant and the polar director varies across the cell. The polar director structure inside the cell is determined by a competition among the torques due to the bulk elasticity, electrostatic effects and surface anchoring. The equilibrium profile structure of the polar director is obtained by minimization of the free energy. We find the polar director profile in a cell as a function of the type and strength of the surface anchoring, bulk elastic constants and cell thickness. The effect of the external electric bias field on the structure in the cell is studied, as well. Bent-core molecules have a permanent electric dipole moment. In the external electric field the electric torque tends to rotate the dipoles in the direction of the external field. The polar director profile in the cell in external bias field thus depends on the competition among three effects: anchoring at the surfaces, the elastic properties of the bulk and the influence of the external electric field. By the rotation of molecules in the external electric field, optical properties of the cell are changed, therefore the SmAP$_F$ phase is a promising phase for use in displays with high response time, high contrast, continuous gray level and wide viewing angle. The response of the SmAP$_F$ phase to an alternating external electric field (the dielectric response) is also considered. The dielectric response of the SmAP$_F$ phase consists of two modes: the phase and amplitude mode. The phase mode is due to fluctuations in the orientation of the local direction of the spontaneous polarization and the amplitude mode is due to the change in the magnitude of spontaneous polarization. The frequency of the phase and amplitude mode and the dielectric permittivity are calculated numerically as a function of the bias external DC electric field, cell thickness, the type and strength of surface anchoring and the ratio between the bend and splay elastic constants. Analytical solution for a very specific case of chosen parameters is also obtained. Theoretically obtained dependencies are in agreement with the reported experimental measurements. In the thesis we study the effect of different types of surface anchoring and for this purpose three different types of cells are defined. The polar director profile and the dielectric response is calculated in all three types of cells. The type I cell has polar surface anchoring of equal strengths at both surfaces. The type II cell has, in addition to the polar surface anchoring of equal strengths at both surfaces, a nonpolar anchoring at the bottom surface. The type III cell has polar surface anchoring at both surfaces but not of equal strengths. We predict that by comparison of the dielectric response of the SmAP$_F$ phase in all three types of cells the type of the polarization splay in bent-core liquid crystals can be determined. The thesis is divided into three parts. In the first part the basic physical properties of ferroelectric liquid crystals, focusing on the bent-core liquid crystals, are discussed. In the second part phenomenological theoretical model is developed. In the third part of the thesis a dielectric response in external bias field is studied.
Keywords: Bent-core liquid crystals, ferroelectric smectic-A phase, dielectric response, confined geometry, phenomenological continuum model, surface anchoring, polarization splay
Published in DKUM: 06.05.2016; Views: 1536; Downloads: 136
.pdf Full text (4,05 MB)

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