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This manuscript demonstrates the well-posedness (existence, uniqueness, and regularity of solutions) of the Cauchy problem for simplified equations of nematic liquid crystal hydrodynamic flow in three dimensions for initial data that is uniformly locally L3(R3) integrable (L3U(R3)). The equations examined are a simplified version of the equations derived by Ericksen and Leslie. Background on the continuum theory of nematic liquid crystals and their flow is provided as are explanations of the related mathematical literature for nematic liquid crystals and the Navier–Stokes equations.

This manuscript demonstrates the regularity and uniqueness of some geometric heat flows with critical nonlinearity. First, under the assumption of smallness of renormalized energy, several issues of the regularity and uniqueness of heat flow of harmonic maps into a unit sphere or a compact Riemannian homogeneous manifold without boundary are established. For a class of heat flow of harmonic maps to any compact Riemannian manifold without boundary, satisfying the Serrin's condition, the regularity and uniqueness is also established. As an application, the hydrodynamic flow of nematic liquid crystals in Serrin's class is proved to be regular and unique. The natural extension of all the results to the heat flow of biharmonic maps is also presented in this manuscript.

L’objectif de ce travail est d’étudier les transitions de phases sol-gel et isotrope-nématique dans des suspensions de smectites dioctaédriques en fonction de la morphologie et de la nature minéralogique des argiles. Bien que tous les systèmes étudiés présentent une transition sol-gel à de faibles fraction volumique, la transition cristal-liquide isotrope-nématique n’a pu être identifiée que dans le cas de suspensions de smectites ayant un déficit de charge tétraédrique. L’effet de la localisation de la charge sur le comportement colloïdal a été déterminée à l’aide de la diffusion des rayons X aux petits angles (SAXS) et par des mesures rhéologiques. La nature des interactions électrostatiques dans ces suspensions est purement répulsive et rejette l’idée d’une structure tridimensionnelle de type « château de carte ». Cependant, les smectites ayant un déficit de charge tétraédrique sont plus répulsives et ont des propriétés viscoélastiques plus faibles que celles ayant un déficit octaédrique. Il a également été montré que la dépendance en taille de particules de la position de la transition sol-gel était liée à une statistique de piégeage hydrodynamique des plaquettes d’argile. Finalement, l’application de champs externes (électrique et magnétique) a permis d’obtenir l’alignement de la phase nématique tandis que dans la phase isotrope, le champ électrique induit un ordre antinématique parfait. Afin de préserver l’ordre induit, ces suspensions ont été polymérisées sous champ permettant l’obtention de nanocomposites orientées et structurés / The aim of this work is to study sol-gel and isotropic-nematic phases transitions in suspensions of dioctahedral smectites depending on the morphology and mineralogical nature of clays. Although all the systems studied exhibit a sol-gel at low volume fraction, the liquid-crystalline isotropic-nematic transition could be identified only in the case of smectites with tetrahedral charge deficit. The effect of charge location on the colloidal behavior was determined using small-angle X-ray scattering (SAXS) and rheological measurements. The nature of electrostatic interactions in these suspensions is purely repulsive and rejects the idea of the so-called “house of card” network. However, smectites with a charge deficit located in the tetrahedron are more repulsive and their viscoelastic properties are lower than octahedrally substituted clays. It was also shown that the particle size dependence of the volume fraction corresponding to the sol-gel transition c was related to a simple statistical hydrodynamic trapping of clay platelets. Finally, the application of external fields (electric and magnetic) has resulted in the alignment of the nematic phase while in the isotropic phase, the electric field induces a perfect antinematic order. To preserve the induced alignment, these suspensions were polymerized under the field to obtain perfectly aligned and patterned nanocomposites

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Orientador: Eduardo Granado Monteiro da Silva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-01T17:31:34Z (GMT). No. of bitstreams: 1 Kaneko_UlissesFerreira_D.pdf: 51229533 bytes, checksum: 3d39a6722771458fa1812d75c31661b4 (MD5) Previous issue date: 2017 / Resumo: Nesta tese, empregamos espectroscopia Raman para realizar um estudo detalhado dos fônons e das respostas eletrônicas em monocristais de LaFeAsO. Nós observamos as simetrias e frequências dos fônons nas fases tetragonal e ortorrômbica e também a dependência com a temperatura de um pico quase-elástico (do inglês: QEP) na simetria B1g com intensidade máxima em torno da transição magnética TN . A área e a altura do QEP B1g foram atribuídas às flutuações nemáticas de spin, enquanto que a largura do QEP B1g foi relacionada com taxa de relaxação dessas flutuações. Através da análise da largura do QEP B1g propomos que a transição estrutural esté relacionada a um congelamento gradual das flutuaçõees nemáticas de spin, o que deve ser um fenômeno geral presente nos demais supercondutores à base de Fe. Esse estudo foi complementado por medidas de espectroscopia Raman em BaFe2As2 e de difração de raios-X com luz síncrotron em LaFeAsO, BaFe2As2 e SrFe2As2 dopado com Co. Paralelamente, nós estudamos as estruturas cristalinas e magnéticas em compostos da série Ba1?xLaxTi1/2Mn1/2O3 através da técnica de difração de nêutrons / Abstract: In this thesis, we employed Raman spectroscopy to perform a detailed study of the phonons and electronic responses in single crystals of the LaFeAsO. We observed the symmetries and frequencies of the phonons in the tetragonal and orthorhombic phases and also the temperature dependence of the quasi-elastic peak (QEP) in the B 1g symmetry with maximum intensity around the magnetic transition T N . The B 1g QEP area and height were ascribed to spin nematic fluctuations, while the B 1g QEP width was related to the relaxation rate of these fluctuations. From the B 1g QEP width analysis we propose that the structural transition is related to a gradual freezing of the spin nematic fluctuations, which may be a general phenomenon present in other Fe-based superconductors. This study was complemented by measurements of Raman spectroscopy in BaFe2As2 and synchrotron X-ray diffraction in LaFeAsO, BaFe2As2 and Co-doped SrFe2As2 . In parallel, we studied the crystal and magnetic structures in compounds of the series Ba1?xLaxTi1/2Mn1/2O3 through the neutron diffraction technique / Doutorado / Física / Doutor em Ciências / 140978/2012-7 / CNPQ

The recent interest in bent core liquid crystal has shown many unique physical properties, such the anomalous behaviour of the elastic constants (SplayK1, Twist K2, and BendK3). In bent core liquid crystals it is observed that K3K1). Such behaviour is analogous to calamitic liquid crystals but is in contrast to all other bent-core nematic materials reported to date. Such a result questions some of the current explanations for the elastic behaviour of bent-core materials. Using molecular field theory and atomistic modelling the different elastic behaviour predicted is again in excellent agreement with experimental results. The bend angle is again shown to be an important part in determining the physical properties of bent-core nematic liquid crystals. In a mixture from an oxadiazole dopant and calamitic host liquid crystal, it was found that a filament structure appears in the nematic phase. The filaments appear to interfere with the measurements for elastic constants. In order to understand the filament structure many methods were used including SAXS, dielectric permittivity, and DSC. It was found that the mixture had formed a gel - like phase. The gel is composed of a liquid crystal network and a liquid crystal background, not seen before in any gel system. Due to the liquid crystalline properties both the network and the background can be aligned and manipulated. The new gel phase can possess many new unique properties which warrant further studies understand further into how fundamentally the phase is forming.

This thesis presents the investigation of the liquid crystal (LC) - particle suspensions. Particles from nano- to micro-size, spherical to two-dimensional shapes, with different functionality are dispersed into nematic and smectic phases. The aim is to create ordered nanoparticle (NP) assemblies and thereby modify the common properties of the liquid crystal, such as dielectric anisotropy and electro-optical, revealing any interaction between particles and LC properties. It is found that for concentrations (>0.5vol%), the ferroelectric NPs have increased the sensitivity of the nematic liquid crystal to the electric field through electro-optical responses, which is seen by an enhancement in the dielectric anisotropy. This could be induced by the coupling of the electrical dipole moments in the spherical NPs with the LC director field. The electro-optical properties of the chiral smectic (SmC*) phase (tilt angle Θ, switching time τ_s and spontaneous polarisation P_s) are found to be independent of the concentration and sizes of the doped NPs. The relaxation frequency f_R of the Goldstone mode is faster in the ferroelectric NPs suspensions of 2.0vol% compared to the paraelectric NPs. In the graphene oxide (GO) - nematic LC (5CB) suspensions, the small GO sizes of mean size 560 nm are more easily dispersible than larger flakes of 2.8 micro metre mean size. As the GO concentration is increased, each of the threshold voltage and splay elastic constant dramatically increases, reaching saturation at ≈1.0wt%. The field driven switching-on time is practically not affected, while the purely elastically driven switching-off time is strongly sped-up. Interestingly, thermotropic and lyotropic LC phases are exhibited in the GO-5CB suspensions when heating the thermotropic liquid crystal into its isotropic phase. The isotropic phase of 5CB acts as a solvent for the GO particles, forming a lyotropic nematic phase with largely reduced birefringence. It is found that the nematic to isotropic phase transition is shifted toward higher temperature for the GO-5CB system compared to the BaTiO3-5CB system. Dispersions of different sizes of GO flakes are prepared in isotropic and nematic fluid media. The dielectric relaxation behaviour of GO-dispersions was examined for a wide temperature range (25-60 ℃) and frequency range (100 Hz-2 MHz). The mixtures containing GO flakes were found to exhibit varying dielectric relaxation processes, depending on the size of the flakes and the elastic properties of the dispersant fluid. The relaxation frequencies in the isotropic media were lower compared to the nematic medium. Relaxation frequencies (~10 kHz) are observed in the GO-isotropic media, which are reduced as the size of the GO flakes are decreased, are anticipated to be inherited from GO flakes. However, the fast relaxations (~100 kHz) that are observed in the nematic suspensions could imply strongly slowed down molecular relaxation modes of the nematogenic molecules. Finally, the phase diagram of lyotropic LC as a function of the lateral dimensions of the GO flakes, their concentration, geometrical confinement configuration and solvent polarity was investigated. Polarising optical microscopy was used to determine isotropic-biphasic-nematic phase evolution. The confinement volume and geometry of the sample relative to the GO size are shown to be vital to the observation of the lyotropic phase. GO LCs have the potential for a range of applications from display technologies to conductive fibres. The confinement related LC phase transition is critical toward their applications. It is also found that the stability of the LC phase is higher for the solvent of higher dielectric constant.