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Chiral nematic thin films containing responsive dopants have previously been considered as sensors and dosimeters. Some systems have been developed, with mixed results. The investigation so far has been piecemeal, with little attention paid towards understanding the properties that govern how these sensors operate. By carefully considering these properties, we believe that it is possible to predict the effectiveness of a sensor, and therefore a framework can be established which would allow only sensors with significant potential to be investigated. The applications of a variety of chiral nematic thin films incorporating responsive dopants is modelled and then investigated experimentally. The systems chosen for investigation were selected using the criteria of commercial potential and synthetic simplicity. In each case it was found that the behaviour of these systems could be predicted well from simple experimental data. The systems chosen for investigation were judged on the basis of two key criteria: They must be systems that deal with a target that is of commercial interest, so that performance expectations for 'real-life' applications can be given at the start of the research process. They must be manufactured only using materials and processes that are commercially available. These limitations were chosen to highlight the conditions under which such a model would be expected to operate. In this work, a successful model that predicts sensors behaviour from basic experimental information was developed and shown to match well with experimental results. In the process, three new sensing systems were developed, all with potential commercial significance. Additionally, some observations regarding the methods of operation which are most likely to result in high sensitivity and low cross-sensitivity have been made.

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本論文致力於棒狀液晶體動力學系統的幾個方面的研究，其中包括:空間週期問題及初邊值問題弱解的整體存在性，初值問題及初邊值問題強解的局部存在唯一性及相應的爆破準則。 / 首先，借助於一類新的逼近系統，我們證明了非等溫液晶體系統的二維空間週期問題存在整體弱解。與經典的Ginzburg Landau逼近系統不同的是，我們所採用的系統不是奇異型逼近。由於無法從基本能量等式中獲得方向場的二階導數的估計，我們採用局部能量不等式，於局部時間內，重新獲得了這些估計。與等溫系統不同，我們所獲得的弱解保持整體能量不變。由此可以看出，系統所損失的內能和動能全部轉化為熱能。此外，我們所獲得的弱解至多含有限個奇異時間點。而且，在每個奇異時間點上，由於能量集中現象的發生，系統的溫度必然會在某些區域內突然升高。 / 其次，通過Ginzburg- Landau逼近，我們證明了三維Ericksen-Leslie系統的初值問題存在唯一的局部強解，並建立了相應的爆破準則。我們共建立了如下四種爆破準則: (i) Serrin型準則; (ii) Beale-Kato-Majda (縮寫為BKM) 型準則; (iii) 混合型準則，即對速度場和方向場之一提Serrin型條件，而對另一場提BMK型條件;(iv) 一個新型準則，即用Ginzburg-Landau逼近系統的強解的Serrin型範數來刻畫Ericksen- Leslie 系統的強解的最大存在區間。其中，借助於一新的對數型Sobolev不等式，我們對速度場所建立的BKM型條件是經典條件的一個BMO型弱化。此外，我們還證明了，于強解的存在區間內， Ginzburg-Landau系統強收斂至Ericksen- Leslie 系統。 / 然後，我們將我們的關於強解的局部存在唯一性的結果推廣至有界域的情形。我們採用的依舊是Ginzburg-Landau逼近。為克服由於缺乏方向場的法向三階導教估計而帶來的困難，我們採用了一新的Sobolev型嵌入不等式。該嵌入不等式將Sobolev函數嵌入至一適當的混合範教LP 空間。此外，我們亦證明了局部強解的相應爆破準則 。 / 最後，通過利用前述提及的技街，我們證明了二維有界域上Ericksen-Leslie 系統的初邊值問題存在唯一的局部強解並存在一整體弱解。特別地，通過利用局部能量不等式，我們證明了強解的存在區間以及局部時間內的估計只依賴於初值的基本能量及其L²積分連續性。借助於此，通過對強解取極限，我們獲得了Ericksen-Leslie 系統的弱解。 / This thesis is devoted to some studies on the hydrodynamical model of nematic liquid crystals, including: the global existence of weak solutions to the spacial periodic and the initial-boundary value problems, the local well-posedness and blow-up criteria of strong solutions to the Cauchy and the initial-boundary value problems. / First, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system in T², based on a new approximate system. Different from the classic Ginzburg-Landau approximation, this new system is not a singular type one. Local energy inequalities are employed to recover the estimates on the second order spacial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. Different from the isothermal case, the weak solutions we obtained conserve the total energy, and thus the kinetic and potential energies transfer to nothing but the heat energy. Also our weak solutions have at most finite many singular times at which the energy concentration occurs, and as a result, the temperature must increase suddenly at each singular time on some part of T². / Next, we prove the local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in R³, based on the Ginzburg-Landau approximation. Four kinds of blow-up criteria are established, including: (i) the Serrin type; (ii) the Beale-Kato-Majda (BKM for short) type; (iii) a mixed type, i.e., a Serrin type condition for one field and a BKM type condition on the other one; (iv) a new one, which characterizes the maximal existence time of a strong solution to the Ericksen-Leslie system in terms of the Serrin type norms of the strong solutions to the Ginzburg-Landau approximate system. Besides, thanks to a new logarithmic Sobolev type inequality, our BKM type condition for the velocity is a BMO type improvement version. We also show that the strong solutions of the Ginzburg-Landau approximate system converge to a strong solution of the Ericksen-Leslie system up to the maximal existence time of this solution. / Then, we generalize our results on the local well-posedness of strong solutions to the Ericksen-Leslie system for the whole space to bounded domains of R³, still by the Ginzburg-Landau approximation method. A new Sobolev embedding inequality into mixed-norm L{U+1D3E} space is exploited to overcome the difficulty caused by the lack of the uniform estimates on the third order normal derivative of the director field to the Ginzburg-Landau approximate system. We also establish a blow-up criterion of the local strong solutions to the Ericksen-Leslie system. / Finally, using the technics exploited in the previous results, we obtain the local existence of strong solutions and the global existence of weak solutions to the Ericksen-Leslie system in bounded domains of R². In particular, by employing the local energy inequality, we prove that the lower bound of the existence time and the local in time estimates of a strong solution depend only on the basic energy and the L² integral continuity of the initial data. Thanks to these properties, by taking the limit of a sequence of strong solutions, we obtain a weak solution to the Ericksen-Leslie system. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Li, Jinkai. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 179-185). / Abstracts also in Chinese. / Introduction --- p.1 / Chapter 1 --- Global existence of weak solutions to the nematic liquid crystals in T² --- p.14 / Chapter 1.1 --- Introduction and main results --- p.14 / Chapter 1.2 --- Preliminaries --- p.21 / Chapter 1.3 --- Faedo-Galerkin scheme --- p.24 / Chapter 1.4 --- The limit n → ∞ --- p.27 / Chapter 1.5 --- The limit M → ∞ --- p.33 / Chapter 1.6 --- The limit N → ∞ and the local existence --- p.47 / Chapter 1.7 --- The global existence --- p.51 / Chapter 2 --- Local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in R³ --- p.60 / Chapter 2.1 --- Introduction and main results --- p.60 / Chapter 2.2 --- Local existence --- p.67 / Chapter 2.3 --- Blow-up criteria --- p.83 / Chapter 2.4 --- Convergence of Ginzburg-Landau to Ericksen-Leslie --- p.99 / Chapter 3 --- Local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in bounded domains of R³ --- p.112 / Chapter 3.1 --- Introduction and main results --- p.112 / Chapter 3.2 --- Local well-posedness --- p.119 / Chapter 3.3 --- Blow-up criteria --- p.141 / Chapter 4 --- Global existence of weak solutions to the Ericksen-Leslie system in bounded domains of R² --- p.156 / Chapter 4.1 --- Introduction and main results --- p.156 / Chapter 4.2 --- Strong solutions and blow-up criteria --- p.161 / Chapter 4.3 --- Global weak solutions --- p.172 / Chapter 5 --- Discuss on future works --- p.177 / Bibliography --- p.178

Active nematic elastomers are a class of active materials that possess the elasticity of a rubber, and the orientational symmetry of a liquid crystal. Their constituent elements are typically elongated, cross-linked and active. The cross-linking of the elements leads to an elasticity that prevents the material to ow like a liquid. These elements are active in a sense that they continuously consume and dissipate energy, creating a state that is far-from-equilibrium. Active nematic elastomers may be a good physical model for biological systems such as the metaphase spindle, a complex biological machine that is made of an integrated assembly of microtubules and molecular motors. These motors not only cross-link the microtubules, but also actively slide them against each other, creating a highly dynamic, non-equilibrium state. The metaphase spindle, like other non-equilibrium structures in biology, has important functions to perform. During mitosis, the spindle is responsible for (1) capturing the sister chromatids, (2) bringing all the sister chromatids to the equator of the mother cell, and (3) segregating the daughter chromosome to the opposite poles of the cell. Thus, a fundamental challenge to biological physics is to understand the complex dynamics of the spindle, and similar systems, using the tools of non-equilibrium statistical mechanics. In this Thesis, we develop and explore a phenomenological model for an active nematic elastomer. We formulate the dynamics of this phenomenological model by incorporating the contribution of the active elements to the standard formulation of the hydrodynamic equations of a passive system. In a coarse-grained picture, the activity is taken into account as an extra active stress, proportional to the alignment tensor, added to the momentum equation of an otherwise passive nematic elastomer. Having obtained the equations of motion of an active nematic elastomer, we then investigate the response of the system to an external field by means of examining the structure and the stability of the modes. An active nematic elastomer has eight modes, in which six modes are propagating and two modes are massive. Out of the six propagating modes, two modes are in the longitudinal direction, linked to the density waves, and the other four modes are in the transverse direction, linked to the shear waves. The nature of these propagating modes transitions from dissipative and oscillatory, and vice versa, depending on the length scales. In particular, their stability is largely determined in the hydrodynamic limit, by a competition between the stabilizing effect of the elasticity and the destabilizing effect of the activity. In fact, the activity renormalizes the elastic coefficients down to even a negative value in some cases and thus, rendering the system linearly unstable. This is in contrast to the well-known instability of an active nematic liquid crystal, which is always linearly unstable. We then map out and discuss the stability phase diagram of the active nematic elastomer. Next, we compute and study various equal-time correlation functions of an active nematic elastomer, assuming that the noise spectra are thermal in origin. We find that they can be conveniently arranged into two terms. The first term has the exact mathematical structure of the equal-time correlation functions of a passive nematic elastomer, albeit with certain coefficients renormalized by activity. The second term, which is proportional to the activity, represents the non-equilibrium nature of an active nematic elastomer, and manifestly breaks the Fluctuation-Dissipation Theorem. We also find that (1) the displacement-displacement correlation function decays inversely with the square of the wave number for both the compressible and incompressible nematic elastomer, similar to that of a passive nematic elastomer, with elastic coefficients renormalized by the activity. (2) The density-density correlation function approaches a constant at the long wave-length limit, since the conservation of mass links the density to the rate of changes of the displacement in the longitudinal direction. (3) The director-displacement correlation function is purely imaginary, and thus the director is locked to the displacement with a (π/2) phase-shift. (3) The director-director correlation function approaches a constant value in the long-wavelength limit, instead of decaying inversely with the square of the wave number, like it would for a liquid crystal. This is because of the massive mode stems from the coupling energy, and it indicates that director in the large length scale is locked to a specific angle. These theoretical results are in qualitative agreement with the experimental measurements of the spindle. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

A number of compounds were synthesized with the ultimate goal being the synthesis of C₂ symmetric molecules which displayed thermotropic liquid crystalline behaviour. The compounds prepared were 4-alkoxy benzophenones, 3,4-bis-alkoxy benzophenones, 4- alkoxy dibenzylidene acetones, 3,4-bis-alkoxy dibenzylidene acetones and 4-alkoxy- 1, 9-diphenyl-nona-l,3,6,8-tetraen-5-ones. The length of the linear alkoxy side chain was varied from C₆H₁₃ to C₁₂H₂₅. All compounds were characterized by FTIR, ¹H, and ¹³C NMR spectroscopy. Mesophase behaviour of the synthesized compounds was investigated using differential scanning calorimetry and polarizing optical microscopy. It was determined that both the alkoxy side chain length, as well as the number of alkoxy side chains have an effect on the ability of this class of C₂ symmetric compounds to selfassemble into liquid crystalline phases. In addition, the overall core size and extent of conjugation also affected mesophase formation. The mono-alkoxy benzophenones and dibenzylidene acetones were non-mesogenic, while all four of the mono-alkoxy 1,9- diphenyl-nona-l,3,6,8-tetraen-5-ones (alkoxy side chain of lengths C₆H₁₃, C₈H₁₇, C₁₀H₂₁ and C₁₂H₂₅)self-assembled into nematic liquid crystalline phases. Increasing the number of alkoxy side chains from one to two per aromatic moiety helped induce liquid crystalline formation: the corresponding bis-C₆H₁₃ benzophenone and bis-C ₆H₁₃, bis C₈H₁₇, and bis-C₁₀H₂₁ dibenzylidene acetones were mesogenic, displaying smectic A (benzophenone) and nematic (dibenzylidene acetone) mesophases respectively.

This study investigates the optical properties of the twisted-nematic liquid-crystals at oblique directions and their applications. A large difference in the phase retardation and the twisted angle of the TN-LC from different viewing directions occurs at the low voltage regime. The proposed viewing angle switching (VAS) panel is developed using this large optically anisotropic behavior of the TN-LC. The proposed VAS panel is only perceived clearly at normal and downward directions in a narrow viewing angle mode to ensure high privacy protection, it highly promising for mobile device applications.

A number of compounds were synthesized with the ultimate goal being the synthesis of C₂ symmetric molecules which displayed thermotropic liquid crystalline behaviour. The compounds prepared were 4-alkoxy benzophenones, 3,4-bis-alkoxy benzophenones, 4- alkoxy dibenzylidene acetones, 3,4-bis-alkoxy dibenzylidene acetones and 4-alkoxy- 1, 9-diphenyl-nona-l,3,6,8-tetraen-5-ones. The length of the linear alkoxy side chain was varied from C₆H₁₃ to C₁₂H₂₅. All compounds were characterized by FTIR, ¹H, and ¹³C NMR spectroscopy. Mesophase behaviour of the synthesized compounds was investigated using differential scanning calorimetry and polarizing optical microscopy. It was determined that both the alkoxy side chain length, as well as the number of alkoxy side chains have an effect on the ability of this class of C₂ symmetric compounds to selfassemble into liquid crystalline phases. In addition, the overall core size and extent of conjugation also affected mesophase formation. The mono-alkoxy benzophenones and dibenzylidene acetones were non-mesogenic, while all four of the mono-alkoxy 1,9- diphenyl-nona-l,3,6,8-tetraen-5-ones (alkoxy side chain of lengths C₆H₁₃, C₈H₁₇, C₁₀H₂₁ and C₁₂H₂₅)self-assembled into nematic liquid crystalline phases. Increasing the number of alkoxy side chains from one to two per aromatic moiety helped induce liquid crystalline formation: the corresponding bis-C₆H₁₃ benzophenone and bis-C ₆H₁₃, bis C₈H₁₇, and bis-C₁₀H₂₁ dibenzylidene acetones were mesogenic, displaying smectic A (benzophenone) and nematic (dibenzylidene acetone) mesophases respectively.

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