Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

The theory and computation of line defects are discussed in the context of both solids and liquid crystals. This dissertation includes four parts. The Generalized Disclination theory is discussed and applied to numerous interfacial and bulk line defect problems. An augmented Oseen-Frank energy as well as a novel 2D-model is proposed and demonstrated for disclination dynamics in liquid crystal. A model based on kinematics and thermodynamics is devised to predict tactoid dynamics during the process of the isotropic-nematic phase transition in LCLC. In the first part of the thesis, the utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived. In the second part, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of various line defects and grain/phase boundary problems are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclinationdipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics (plus kinetics) in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. In the third part, nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. A novel 2D-model of disclination dynamics in nematics is proposed, which is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. In the fourth part, the isotropic-nematic phase transition in chromonic liquid crystals is studied. We simulate such tactoid equilibria and dynamics with a model using degree of order, a variable length director as state descriptors, and an interfacial descriptor. We introduce an augmented Oseen-Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A strategy is devised based on continuum kinematics and thermodynamics. The model is used to predict tactoid dynamics during the process of phase transition. We reproduce observed behaviors in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy constants on the interaction of interfacial and bulk fields in the tactoids.

Chiral nematic liquid crystals or cholesteric liquid crystals (CLC) can be obtained by adding a chiral dopant into a nematic liquid crystal. Liquid crystal molecules spontaneously rotate along a long axis to form helical structures in CLC system. Both pitch size and orientation of the helical structure is determined by the boundary conditions and can be further tuned by external stimuli. Particularly, the uniform lying helical structure of CLC has attracted intensive attention due to its beam steering and diffraction abilities. Up to now, studies have worked on controlling the in-plane orientation of lying helix through surface rubbing and external stimuli. However, it remains challenging to achieve steady and uniform lying helical structure due to its higher energy, comparing with other helical configurations. Here, by varying the surface anchoring, uniform lying helical structure with long-range order is achieved as thermodynamically stable state without external support. Poly (6-(4-methoxy-azobenzene-4'-oxy) hexyl methacrylate) (PMMAZO), a liquid crystalline polymer, is deposited onto the silicon substrate to fine-tune the surface anchoring. By changing the grafting density of PMMAZO, both pitch size and orientation of lying helical structure are precisely controlled. As the grafting density increases, the enhanced titled deformation of helical structure suppresses the pitch size of CLC at the same cell thickness; as the cell thickness increases, the morphology transition from long-range order stripe to small fingerprint domain is facilitated.

No description available.

Eksperimentai buvo atliekami su bandinėliais gautais iš Madrido, Maskvos ir St.Peterburgo, tai yra su fotoniniais kristalais. Darbe buvo nagrinėta fotoninio kristalo opalo struktūrą ir optines savybes draustinės stop juostos srityje bei defektų valdymo būdai, keičiant elektrinį lauką. Nagrinėjamas elektrinio lauko poveikis defektams, stop juostai. Nustatyta, kad elektriniame lauke susikuria defektai, kuriuos galima valdyti nuo 0V iki 7V įtampos intervale. Išmatuoti defektinės modos perjungimo laikai kurie sieka 200 s, tai 10 kart greičiau nei stop juostos. / We did structural and spectroscopic studies of bulk and thin film synthetic opal. Demonstrate that the photonic crystal, opal have defects, but these defects may be "good" when use it to control light in stop band.

Esta pesquisa mostrou a viabilidade técnica da utilização de células de cristais líquidos nemáticos (CLNs) como elementos sensores eletro-ópticos de tensões elétricas eficazes (RMS). Duas foram as filosofias abordadas na concepção desses sensores: a modulação em amplitude da intensidade da luz polariza atuando em células transmissivas e a tensão de Freedericksz atuando em células reflexivas. Os sensores baseados na primeira filosofia foram denominados, nesta pesquisa, de sensores de escala de cinza (EC) e os segundos de sensores de gráfico de barras (GB). O sensor EC foi desenvolvido para aplicações em altas tensões. Este sensor é constituído por um divisor de tensão capacitivo, onde o braço de baixa tensão é composto por uma célula de cristal nemático torcida (CLNT). O sensor EC alia as vantagens dos tradicionais sistemas eletro-ópticos, tais como a imunidade às interferências eletromagnéticas (IEM); o alto isolamento elétrico proporcionado pela fibra óptica; com as vantagens de ser um sistema com um simples aparato óptico, então indutivo. O sensor GB mostrou-se mais versátil que o sensor EC. Neste sensor o braço de alta tensão do divisor de tensão capacitivo foi confeccionado na própria célula. Além disso, o sensor GB é menos sensível a influências térmicas, sendo neste caso mais indicado para aplicações de campo. Além das vantagens citadas acima, os sensores desenvolvidos apresentam as características de possuírem baixo custo, facilidade de instalação, versatilidade e empregarem tecnologia nacional. Também neste trabalho, foram estudados e determinados modelo físicos e elétricos que melhor representam o comportamento das células de CLNs. Os modelos físicos permitiram expandir o conhecimento sobre o comportamento de dispersão dielétrica presente nestes materiais devido ao movimento de impurezas iônicas; ao movimento molecular, e ao acúmulo de cargas espaciais nas interfaces entre as camadas de alinhamento e o cristal líquido, e também, auxiliaram na compreensão dos parâmetros físicos que influenciam no comportamento anisotrópico da permissividade dielétrica e da condutividade elétrica dos CLNs. Os modelos elétricos, além de auxiliarem na compreensão dos mecanismos físicos auxiliando com isso a proposição de modelos fenomenológicos, também mostraram-se uma poderosa ferramenta a ser aplicada na otimização de processos de fabricação e no desenvolvimento de dispositivos utilizados na confecção de mostradores de informação (LCDs). Estes modelos elétricos foram testados e utilizados em programas computacionais dedicados à simulação de circuitos elétricos, e puderam auxiliar sobremaneira no desenvolvimento do sensor GB. / In this research the technical viability of the usage of nematic liquid crystal (NLC) cells as sensor elements of effective electric voltage (RMS) is presented. Two approaches were adopted for the conception of these sensors: the modulation in width of the intensity of the polarized light acting in transmissive cells and the voltage of Freedericksz acting in reflexive cells. The sensors based on the first approach were termed grayscale sensors and the second were bargraph sensors. A grayscale sensor was developed for applications in high voltage. This sensor is constituted by a capacitor voltage divider, where the low voltage arm is composed of a cell of twisted nematic liquid crystal (TNLC). The grayscale sensor combines the advantages of traditional electro-optical systems, such as immunity to the electro-magnetic-interference (EMI) and the high electric insulation provided by the optical fiber; associated to characteristics of being a simple optical apparatus and a non-inductive system. The bargraph sensor has shown to be more versatile than the grayscale sensor. In this bargraph sensor the high voltage arm of the capacitor voltage divider was built in the CLNT cell itself, facilitating its use in both high and low voltages. Besides, the bargraph sensor is less sensitive to thermal influences, being in this case more suitable to field applications. In addition to the advantages mentioned above, both sensors developed showed characteristics of low cost, installation easiness, versatility and indigenous technology. Due to the need of establishing parameters for the development of the electric voltage sensor, also in this research, physical and electric models that best represent the behavior of NLC cells were obtained. The physical models allowed expanding the knowledge about the behavior of dielectric dispersion present in these materials due to the movement of ionic impurities, molecular movement, and the accumulation of space charge in the interfaces between the alignment layers and the liquid crystal. These models have also contributed to the understanding of the physical parameters that influence the anisotropic behavior of both dielectric permittivity and electric conductivity of NLCs. Besides, the electric models helped in the understanding of the physical mechanisms aiding in the proposition of phenomenological models. They have also proved to be a powerful tool to be applied in the optimization of production processes, as well as in the development of devices used in liquid crystal displays (LCDs). These electric models were tested and used in software for the simulation of electric circuits and could aid greatly in the development of bargraph sensors.

A major area of research recently has been the study of nonlinear waves in liquid crystals. The availability of commercial liquid crystals and the formation of solitons at mWpower levels has meant that experimental research and the need to understand how the solitons are formed and interact has been boosted. The first part of the thesis looks at how two laser beams in a nematic liquid crystal interact. Specifically research has centred on the problem of directing a signal beam to a target area by varying the input angle of the control beam. Different approximate models are developed to describe this phenomena, with the results from these models compared to a full numerical analysis. The first model developed is called the particle model and is based on the unmodified modulation equations. The results from this model were acceptable when compared with the results obtained from a full numerical analysis. This comparison is indicative that the underlying assumptions of the model did not capture an essential part of interaction between the two laser beams. The second model used to describe the interaction between the two laser beams was based on the law of conservation of momentum in the laser beams. Here the potential between the laser beams was modified to take into account the profile of the beams. The results from this model were in excellent agreement with results from the full numerical analysis, showing the key role potential between the beams plays in the trajectories of the beams. The interaction between dark solitons was also studied. The model used in this case was based on the modulation equations with a suitable trial function for dark solitons. The results from this model were in excellent agreement with the results from the full numerical analysis. The behaviour of the dark solitons shown by the approximate model and the full numerical analysis showing similar key features. This thesis sets out the equations describing the interaction of laser beams in liquid crystals. These are the equations used to carry out a full numerical analysis. This analysis is valuable in its own right and is the standard to compare the results obtained from other models but to achieve a deeper understanding of how laser beams interact in liquid crystals approximate models are developed so that the important parameters in each model can be identified. The Lagrangian describing the interaction of laser beams in liquid crystals is used in all the approximate models. The approximate models can then be developed through the use of suitable trial functions that adequately describe how the laser beams interact. The derivation of the equations and how these equations are solved is described for each model. The results from each model are compared to a full numerical analysis with a discussion of how the results compare.

Esta pesquisa mostrou a viabilidade técnica da utilização de células de cristais líquidos nemáticos (CLNs) como elementos sensores eletro-ópticos de tensões elétricas eficazes (RMS). Duas foram as filosofias abordadas na concepção desses sensores: a modulação em amplitude da intensidade da luz polariza atuando em células transmissivas e a tensão de Freedericksz atuando em células reflexivas. Os sensores baseados na primeira filosofia foram denominados, nesta pesquisa, de sensores de escala de cinza (EC) e os segundos de sensores de gráfico de barras (GB). O sensor EC foi desenvolvido para aplicações em altas tensões. Este sensor é constituído por um divisor de tensão capacitivo, onde o braço de baixa tensão é composto por uma célula de cristal nemático torcida (CLNT). O sensor EC alia as vantagens dos tradicionais sistemas eletro-ópticos, tais como a imunidade às interferências eletromagnéticas (IEM); o alto isolamento elétrico proporcionado pela fibra óptica; com as vantagens de ser um sistema com um simples aparato óptico, então indutivo. O sensor GB mostrou-se mais versátil que o sensor EC. Neste sensor o braço de alta tensão do divisor de tensão capacitivo foi confeccionado na própria célula. Além disso, o sensor GB é menos sensível a influências térmicas, sendo neste caso mais indicado para aplicações de campo. Além das vantagens citadas acima, os sensores desenvolvidos apresentam as características de possuírem baixo custo, facilidade de instalação, versatilidade e empregarem tecnologia nacional. Também neste trabalho, foram estudados e determinados modelo físicos e elétricos que melhor representam o comportamento das células de CLNs. Os modelos físicos permitiram expandir o conhecimento sobre o comportamento de dispersão dielétrica presente nestes materiais devido ao movimento de impurezas iônicas; ao movimento molecular, e ao acúmulo de cargas espaciais nas interfaces entre as camadas de alinhamento e o cristal líquido, e também, auxiliaram na compreensão dos parâmetros físicos que influenciam no comportamento anisotrópico da permissividade dielétrica e da condutividade elétrica dos CLNs. Os modelos elétricos, além de auxiliarem na compreensão dos mecanismos físicos auxiliando com isso a proposição de modelos fenomenológicos, também mostraram-se uma poderosa ferramenta a ser aplicada na otimização de processos de fabricação e no desenvolvimento de dispositivos utilizados na confecção de mostradores de informação (LCDs). Estes modelos elétricos foram testados e utilizados em programas computacionais dedicados à simulação de circuitos elétricos, e puderam auxiliar sobremaneira no desenvolvimento do sensor GB. / In this research the technical viability of the usage of nematic liquid crystal (NLC) cells as sensor elements of effective electric voltage (RMS) is presented. Two approaches were adopted for the conception of these sensors: the modulation in width of the intensity of the polarized light acting in transmissive cells and the voltage of Freedericksz acting in reflexive cells. The sensors based on the first approach were termed grayscale sensors and the second were bargraph sensors. A grayscale sensor was developed for applications in high voltage. This sensor is constituted by a capacitor voltage divider, where the low voltage arm is composed of a cell of twisted nematic liquid crystal (TNLC). The grayscale sensor combines the advantages of traditional electro-optical systems, such as immunity to the electro-magnetic-interference (EMI) and the high electric insulation provided by the optical fiber; associated to characteristics of being a simple optical apparatus and a non-inductive system. The bargraph sensor has shown to be more versatile than the grayscale sensor. In this bargraph sensor the high voltage arm of the capacitor voltage divider was built in the CLNT cell itself, facilitating its use in both high and low voltages. Besides, the bargraph sensor is less sensitive to thermal influences, being in this case more suitable to field applications. In addition to the advantages mentioned above, both sensors developed showed characteristics of low cost, installation easiness, versatility and indigenous technology. Due to the need of establishing parameters for the development of the electric voltage sensor, also in this research, physical and electric models that best represent the behavior of NLC cells were obtained. The physical models allowed expanding the knowledge about the behavior of dielectric dispersion present in these materials due to the movement of ionic impurities, molecular movement, and the accumulation of space charge in the interfaces between the alignment layers and the liquid crystal. These models have also contributed to the understanding of the physical parameters that influence the anisotropic behavior of both dielectric permittivity and electric conductivity of NLCs. Besides, the electric models helped in the understanding of the physical mechanisms aiding in the proposition of phenomenological models. They have also proved to be a powerful tool to be applied in the optimization of production processes, as well as in the development of devices used in liquid crystal displays (LCDs). These electric models were tested and used in software for the simulation of electric circuits and could aid greatly in the development of bargraph sensors.

No description available.

Dans cette thèse, l'interaction entre les grains colloïdaux avec une ligne de disclinaison dans un cristal liquide nématique est explorée. Deux types de colloïdes ont été utilisés; sphérique (billes de silice) et allongé (nanotubes de carbone). En plus, différents types d'ancrage sur leur surface sont obtenus; planaire, homéotrope, et Janus (moitié planaire - moitié homéotrope). Ces paramètres ont été modifiés dans le but d'examiner et d'évaluer la force nématique agissant entre les grains colloïdaux et la ligne de disclinaison, qui est le résultat de l'interaction élastique entre les deux. Cette force est de l'ordre du pico-Newton et capable d'attirer et de fixer les colloïdes dispersés dans le cristal liquide nématique sur la ligne de disclinaison. Une fois que les colloïdes sont fixés sur la ligne de disclinaison, ils peuvent être collés ensemble par électropolymérisation de pyrrole. Ce qui donne lieu à un nanofil conducteur en 3 dimensions, qui est auto-assemblé et auto-connecté à des électrodes prédéfinies à l'intérieur du cristal liquide nématique. / Throughout this thesis, the interaction between the colloidal grains with a disclination line in a nematic liquid crystal is explored. Two types of colloids were used; spherical (silica beads) and elongated (carbon nanotubes). In addition different types of anchoring conditions on their surface is obtained; planar, homeotropic, and Janus (half planar – half homeotropic). These parameters were varied in the aim to examine and evaluate the nematic force acting between the colloidal grains and the disclination line, which is a result of the elastic interaction between the two respectively. This force is in the order of pico-newton, and capable of attracting and fixing the dispersed colloids, in the nematic liquid crystal, on the disclination line. Once the colloids are fixed on the disclination line, they can be glued together by means of electropolymerization of pyrrole. This gives rise to a 3 dimensional conductive nanowires, which are auto-assembled, and auto-connected to predesigned electrodes inside the nematic liquid crystal.