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Impact of curvature on nematic topological defects
Luka Mesarec, 2018, doktorska disertacija

Opis: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We analyze the impact of extrinsic and intrinsic curvature on positions of topological defects (TDs) in two-dimensional (2D) nematic films. We demonstrate that both these curvature contributions are commonly present and are expected to be weighted by comparable elastic constants. A simple Landau-de Gennes approach in terms of tensor nematic order parameter is used to numerically demonstrate impact of the curvatures on position of TDs on 2D ellipsoidal nematic shells. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs (defect,antidefect) on curved surfaces. Furthermore, we estimate a critical depinning threshold to form pairs (defect,antidefect) using the electrostatic analogy. Finally, we show how one could efficiently switch among qualitatively different structures by using a relative volume of ordered shells, which represents a relatively simple naturally accessible control parameter. In doctoral thesis, we developed theoretical model of erythrocyte membrane by using a hybrid Helfrich-Landau type mesoscopic approach, taking into account in-plane membrane ordering. We demonstrate that the derived extrinsic membrane energy term, which strongly depends on the local orientations of the molecules, is essential for the predicted broadening of the range of the relative volumes corresponding to the stable discocyte shapes, which is otherwise very narrow if only intrinsic curvature energy term dominates.
Ključne besede: Topological defects, Continuum fields, Nematic liquid crystals, Biological membranes, Nematic shells, Landau-de Gennes formalism, Topological charge, Nanoparticles, Gaussian curvature, Electrostatic analogy, Intrinsic curvature, Extrinsic curvature, Crystal growth nucleation, Relative volume
Objavljeno: 09.03.2018; Ogledov: 1174; Prenosov: 102
.pdf Celotno besedilo (23,66 MB)

Ferroelectric smectic-A phase made of bent-core liquid crystals: Structure and Dielectric response in thin cells
Kristina Leskovar, 2016, doktorska disertacija

Opis: 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.
Ključne besede: Bent-core liquid crystals, ferroelectric smectic-A phase, dielectric response, confined geometry, phenomenological continuum model, surface anchoring, polarization splay
Objavljeno: 06.05.2016; Ogledov: 1236; Prenosov: 106
.pdf Celotno besedilo (4,05 MB)

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