<div>This thesis mainly focuses on the PDE theories that arise from the study of hydrodynamics of nematic liquid crystals. </div><div><br></div><div>In Chapter 1, we give a brief introduction of the Ericksen--Leslie director theory and Beris--Edwards <i>Q</i>-tensor theory to the PDE modeling of dynamic continuum description of nematic liquid crystals. In the isothermal case, we derive the simplified Ericksen--Leslie equations with general targets via the energy variation approach. Following this, we introduce a simplified, non-isothermal Ericksen--Leslie system and justify its thermodynamic consistency. </div><div><br></div><div>In Chapter 2, we study the weak compactness property of solutions to the Ginzburg--Landau approximation of the simplified Ericksen--Leslie system. In 2-D, we apply the Pohozaev type argument to show a kind of concentration cancellation occurs in the weak sequence of Ginzburg--Landau system. Furthermore, we establish the same compactness for non-isothermal equations with approximated director fields staying on the upper semi-sphere in 3-D. These compactness results imply the global existence of weak solutions to the limit equations as the small parameter tends to zero. </div><div><br></div><div>In Chapter 3, we establish the global existence of a suitable weak solution to the co-rotational Beris–Edwards system for both the Landau–De Gennes and Ball–Majumdar bulk potentials in 3-D, and then study its partial regularity by proving that the 1-D parabolic Hausdorff measure of the singular set is 0.</div><div><br></div><div>In Chapter 4, motivated by the study of un-corotational Beris--Edwards system, we construct a suitable weak solution to the full Ericksen--Leslie system with Ginzburg--Landau potential in 3-D, and we show it enjoys a (slightly weaker) partial regularity, which asserts that it is smooth away from a closed set of parabolic Hausdorff dimension at most 15/7.</div>

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22822号 / 理博第4632号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 山本 潤, 教授 佐々 真一, 准教授 荒木 武昭 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This project consists of two parts. One area of focus in the first part is understanding the interactions between a non-ionic, block copolymer type dispersant and hydrophobically-modified, ethoxylated urethane (HEUR) associative thickeners in water. The dispersant was mixed at various concentrations (0-2% by weight) with HEUR thickeners at 1% by weight concentration in the aqueous medium. This study is an integral part of our attempts to determine mechanisms of viscosity drop when colorant dispersions are added to latex tint base formulations thickened with associative thickeners. One of the HEUR thickeners is a product that has been available for over three decades (HEUR RM-825), whereas the other, HEUR RM-995 is a product recently introduced to minimize the tint base viscosity drop. The old HEUR showed a definitive viscosity maximum as a function of the dispersant concentration. However, the new generation product did not indicate a viscosity maximum within the dispersant concentration range studied; instead it showed a small, but linear increase in viscosity as dispersant level was increased. The next area of focus was on understanding the phase behavior, rheology, and interactions between polymer latex particles and a hydrophobically-modified, ethoxylated urethane (HEUR) associative thickener in water. The influence of the addition of surfactant in some of the systems was also studied. Several types of dispersions were made using two types of polymer latex, two associative thickeners, and two surfactants. Mixtures containing a small particle size acrylic latex and HEUR RM-825 exhibited the most interesting and complex phase behavior and rheology. In experiments wherein the latex particle volume fraction was kept constant, the addition of HEUR caused stable, followed by phase separated (syneresis) and stable mixtures as HEUR concentration was increased. The observed phase behavior is consistent with previous work reported by other investigators. However, detailed rheological data on systems such as these have not been reported, and this report presents the rheological data and correlate rheology with the phase behavior. The stable latex-HEUR mixtures at low HEUR levels show shear-thinning viscosity with well-defined low-shear Newtonian plateaus. As HEUR level is increased wherein syneresis is observed, erratic rheological profiles with shear-thickening are observed. When HEUR level is increased to a region where no syneresis is observed, low shear Newtonian plateaus re-appeared albeit at higher viscosities. The effects of added non-ionic and anionic surfactants on the dispersion are also studied. The main focus of the second part of this project is hybrid organic-inorganic photovoltaics. They have been the focus of recent studies due to their promising use in low-cost, flexible electronics, which can be processed from solution by printing and coating techniques. Understanding the rheology of these nanocomposites is essential in controlling shear flows during printing and application processes. Through rheology, we can determine different properties of poly(3-hexylthiophene) and dodecanethiol (DDT) modified zinc oxide (ZnO-DDT). Semiconductor nanowires such as ZnO have rigid or rod-like macromolecule geometry. Therefore, they have a tendency to have a lytropic liquid crystal (LLC) phase. LLC orders occur spontaneously in solutions with rod-shaped or anistropic objects from isotropic phase to nematic phase above a critical volume fraction which was studied using ZnO-DDT. The shear-induced alignment of the liquid crystal molecules was analyzed, serving as a guide for LLC printing. Furthermore by using this nanocomposite we are able to induced gelation using the ZnO-DDT nanowires in what is considered as a “good solvent,” dichlorobenzene. The kinetics of this gelation process was determined to be of first-order reaction kinetics. Furthermore, a mechanism of this gelation process is also presented.

The use of Liquid Crystal (LC) materials, mainly in display applications, has contributed to major advancement in liquid crystal science and technology. New and more complex phases of liquid crystals were developed to compete with conventional nematic LC displays. The challenge now is to manufacture high birefringence liquid crystal materials with low viscosity. LC is also used in many other applications, such as temperature sensors and photonics beam shaping in the form of spatial light modulators (SLM) and q-plates. The first objective of this thesis is to investigate the magic mirror effect using a SLM following Sir Michael Berry’s theory. Here, we demonstrated a simple way of producing the magic mirror effect using LC devices and aimed to use a micron-sized device to shape the phase and polarization of light with gentle phase variation. We were able to generate the magic mirror image intensity pattern, both experimentally and theoretically. This was done by computing and generating the desired phase pattern of an image on the SLM, then aligning light propagation through this phase pattern. The experimental and theoretical results showed good agreement when comparing the produced intensity patterns. In the second part of this thesis, we experimentally investigated the use of structured photons, created using q-plates, which is a birefringent liquid crystal cell of OAM and SAM coupling, in quantum key distribution (QKD) using the BB84 protocol through orbital angular momentum (OAM) maintaining optical fibres. Here, we were successful in generating a secure key between two parties with a quantum bit error rate of 8.6% which is below the security threshold of 11%. This work demonstrates the feasibility of using structured light in QKD through fibres to boost key rates and security.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23224号 / 工博第4868号 / 新制||工||1760(附属図書館) / 京都大学大学院工学研究科高分子化学専攻 / (主査)教授 辻井 敬亘, 教授 秋吉 一成, 教授 竹中 幹人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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