This thesis presents results of novel methodologies applied to oriented systems. Both pure liquid crystalline materials as well as molecules oriented in liquid crystalline matrices have been studied. In particular this thesis presents investigations related to various aspects of NMR in liquid crystalline media, such as, assignment of resonances and the study of director dynamics of spinning liquid crystals in different phases and with different symmetry. Simplified methods for structure determination of solutes dissolved in liquid crystal solvents have been proposed. Diffusion ordered spectroscopy has been used to study a mixture of liquid crystals of opposite diamagnetic susceptibility at its coexistent phase. The methods presented represent novel techniques to characterize the liquid crystalline phase. NMR spectroscopy which has become a method of choice for understanding ordering mechanisms of mesogens requires a robust method for obtaining assignments of the NMR spectra of various nuclei that are found in the mesogens [1, 2]. It turns out that the spectra in the isotropic phase and in the nematic phase of a liquid crystal molecule are very different due to the presence of chemical shift anisotropy in the mesophase spectrum. There are a host of methodologies available for assigning spectra in the isotropic phase [3]. These methods however fail, when applied to the spectrum of the molecules in the mesophase due to the dominating role of strong anisotropic interactions, such as homonuclear couplings among protons. Problems arising while assigning spectral lines of liquid crystals in their nematic phase have been dealt with in chapter 2. To circumvent these problems, a property of the liquid crystal molecules under off-magic angle sample spinning can be utilized. It has been shown by Courtieu et al. [4] that the director/symmetry axis of a Δχ + ve liquid crystal aligns along the spinning axis for θ between 0 ° and θm, where θ is the angle between the spinning axis and the magnetic field and θm = 54.7° is the magic angle. It may be noted that the spectrum of θ = 0° spinning angle corresponds to the normal static spectrum, while the spectrum of θ = θm corresponds to the isotropic spectrum. In an earlier study, Teearr et al. [5] had recorded the 13C liquid crystal spectra as a function of very closely spaced θ values from 90° all the way up to 0°. From these plots of chemical shift versus the angle of spinning, it is possible to follow the trajectory of each 13C line from its position from θ = θm to θ = 0° and then match the spectrum in the isotropic phase (equivalently the magic angle sample spinning spectrum of the nematic phase) to the spectrum of the static sample in the nematic phase. However this method requires recording spectra at closely spaced angle intervals, so that one can unambiguously follow the trajectory of each of the lines without missing out any crossover of trajectories. However, this operation is time consuming. In this thesis we propose an alternate method, where we utilize the fact that the above trajectory has a very distinct relationship to the isotropic and anisotropic chemical shift and the problem of assignment does not require a continuous variation of angles, but just a few selected experiments should enable the assignment of the spectrum in the anisotropic phase. Thus the method of assignment has been made simpler and faster. It is shown that in addition to the assigned isotropic spectrum, only one other Off-magic angle spinning spectrum whose spinning angle θ is accurately known is necessary to obtain the complete assignment of the static spectrum. This procedure is non-trivial due to possibilities of errors in assignments arising out of inaccuracies in the knowledge of chemical shifts and the spinning angle. A computational procedure is proposed to take into account deviations arising out of non-ideal experimental conditions. A discussion regarding the details of the procedure and also situations where there can be ambiguities and how they can be resolved has been elaborated. The developed method has been demonstrated on a well known thermotropic liquid crystalline system, N-(4-ethoxybenzylidene)-4-n-butlyaniline [EBBA]. Since assignment of resonances in the nematic phase is a primary requirement for any further analysis regarding the ordering and deeper understanding of the role of various substituents in the mesogens we believe our novel prescription will be of immense use and utility. The third chapter presents the study of director dynamics in a lyotropic liquid crystal composed of Potassium laurate, 1-Decanol and D2O [6] under variable angle sample spinning using 2H NMR spectrum of D2O. A very interesting interplay of the magnetic orienting torque due to interaction of the liquid crystal director with the magnetic field and viscous torque arising from the viscosity of the sample on the director comes to fore. The relative magnitude of these torques has a direct bearing on the spectral pattern and line shapes observed, providing valuable insights into magnetohydrodynamics of the spinning liquid crystals. This study leads to even more interesting behavior for liquid crystals which deviate from uniaxial symmetry. This competition between magnetic and viscous torques has been quantitatively visualized by simulation of the 2H spectrum. It has been possible to visualize the observed spread in the director distribution arising out of viscous torque in terms of the energetics of the system under fast spinning. If the magnetic torque dominates over the viscous torque, then the equilibrium corresponds to the director orientation of δ = 0° where the energy is at its minimum. However the viscous and magnetic torques can become comparable as it may happen if the spinning angle is close to the magic angle or when the Δχ of the system is small. In those circumstances additional energy from the viscous torque causes the distribution of the director orientation to spread further away from δ = 0° for a positive Δχ liquid crystal. The trigonometric factor [P2(cosθ)∗P2(cosδ)] being proportional to the total energy of the system has been plotted against the spinning angle. The spectrum of the biaxial phase [7] as a function of the spinning angle shows more interesting director distribution. Here the patterns of the director distribution are observed on either side of the magic angle due to the presence of more than one director. The patterns observed also have information about the symmetry of the phase. This work provides insights into magnetohydrodynamics of spinning liquid crystals and can also be of relevance to samples of biological interest such as bicelles with protein oriented in them [8]. The fourth chapter deals with a novel characterization method relevant for the biaxial phase [9]. As an off shoot of the previous chapter, it effectively overcomes the disadvantages of the previous experimental methods which require simulation and line shape fitting to extract useful parameters. The chapter also presents the measurement of geometrical parameters of oriented solutes in phases exhibiting biaxial symmetry. The measured parameters show the effect of the onset of biaxiality as significant deviation in the value of the measured parameter. The utility of liquid crystalline media as solvents in high resolution NMR spectroscopy has been very rewarding since the pioneering work of Saupe and Englert [6]. The intramolecular interactions within solutes are only partially averaged. As a result one obtains a liquid like spectrum while at the same time very useful anisotropic interactions such as dipolar couplings, chemical shift anisotropies, quadrupolar couplings and anisotropic part spin-spin J couplings are extracted [10]. NMR spectra of molecules dissolved in thermotropic liquid crystals have long been used to obtain structural and orientational information. As the same time the complexity of the spectrum increases with the increase in the number of spins and the reduction in symmetry of the molecule, which can make the spectral analysis forbidding. Generally proton spectra have been used to obtain the geometry of the proton skeleton of the molecule and the information that includes dilute X nuclei such as 13C and 15N are available only from satellites which are buried in the intense proton spectrum. Different inequivalent dilute spins coupled to protons form different coupled spin systems in their natural abundance and appear as satellites in the proton spectra. Identification of transitions belonging to each of the spin system is essential to determine heteronuclear dipolar couplings, which is a formidable task. The fifth chapter deals with development of the techniques to obtain the complete structure of the dissolved molecules including nuclei other than protons in their natural abundance. The use of inverse experiments has been elaborated to overcome the problems of sensitivity and complexity for solute molecules having larger number of spins. In the present study using HSQC and HMQC experiments, we have selectively detected spectra of each inequivalent rare spin coupled to protons in pyrazine, pyrimidine and pyridazine dissolved in thermotropic Phase 4 and Phase 5 liquid crystal solvents. This way we could obtain enhancement in the intensity of satellites signals without the interference from the signals connected to the major isotopomers. Besides, we could resolve a complex spectrum into its sub-spectra corresponding to individual 13C and 15N isotopomers. This separation of the spectra corresponding to individual sub-spin systems makes analysis easy and helps analyze larger systems with higher number of spins and lower symmetry. Besides 1H-1H dipolar couplings, 13C-1H and 15N-1H dipolar couplings have been determined in natural abundance, thereby giving the complete dipolar coupling network between all the spins in the molecule. In this treatment pyrazine, pyrimidine and pyridazine have been used as examples of methodology developed. It is expected that the method will be of wider use for several other similar systems. Chapter six describes the diffusion ordered spectroscopic investigation [11] of a phase arising out of mixing together two liquid crystals having opposite signs of diamagnetic susceptibility anisotropy [12]. Towards this end we have used CH3CN as a probe molecule. The spectrum of CH3CN has with it the information about the parallel or perpendicular orientation of the phase. Such a mixture of liquid crystals have shown interesting behavior at the critical temperature where the two phases seem to coexist. It has been an interesting question to understand what exactly happens for the molecular orientation when the macroscopic anisotropy Δχ vanishes. Earlier Jokisaari et al. [13] have varied the temperature very finely taking due precautions to maintain homogeneity and stability of temperature to the tune of ±0.05K across the sample volume. Their observation of a powder pattern exactly in the critical temperature was interpreted as arising out of a distribution of directors equally oriented in all directions. In our experiments we have measured the diffusion coefficient of the probe molecule i.e. acetonitrile as we change the temperature of the system through the critical temperature. At the critical temperature we have a situation of being able to measure the parallel and perpendicular orientational diffusion coefficients simultaneously. The measurements show that the parallel component of the diffusion coefficient has reduced and the perpendicular component has increased in comparison to the trend in the immediate neighboring temperatures, thereby indicating that at the exact critical condition the liquid crystal mixture consists of an isotropic distribution of molecules. As a check to rule out any exchange of molecules in different domains of parallel and perpendicular orientations an EXSY experiment was conducted with a mixing time which was same as that of the diffusion delay in the DOSY experiment. The EXSY spectrum showed no exchange cross peaks between the two orientations, this confirms that the anisotropy of the diffusion vanishes at the critical temperature. Nematic liquid crystals exhibit a rich variety of phases and properties. NMR is a very powerful tool to study the various phases at the microscopic and molecular level. It has also turned out that some of these properties can be usefully utilized for investigation of both small and large molecules by NMR. Thus this thesis has attempted to expand several of the techniques already available for various applications and extend the utility of NMR for the study of partially ordered systems.

Dans le cadre de cette thèse, on s'intéresse à la dynamique de quelques fluides complexes. D'une part on étudie la dynamique des cristaux liquides nématiques, en utilisant les modèles proposés par Ericksen et Leslie, Beris et Edwards, Qian et Sheng. D'autre part, on analyse un fluide complexe dont la dynamique dépend de la température et qui est modélisée par le système de Boussinesq. Les cristaux liquides sont des matériaux avec une phase de la matière intermédiaire entre les liquides et les solides qui sont des phases plus connues. Dans cette thèse, on s'intéresse à l'étude du problème de Cauchy associé à chaque système modélisant leurs hydrodynamiques. Tout d'abord on obtient des résultats d'existence et d'unicité de solutions faibles ou classiques, solutions qui sont globales en temps. Ensuite, on analyse la propagation de la régularité des données initiales pour ces solutions. Le cadre fonctionnel adopté pour les données initiales est celui des espaces de Besov homogènes, généralisant des classes d'espaces mieux connues : les espaces de Soboloev homogènes et les espaces de Hölder. Le système Ericksen-Leslie est considéré dans la version simplifiée proposée par F. Lin et C. Liu, version qui préserve les principales difficultés du système initial. On étudie ce problème en dimension supérieure ou égale à deux. On considère le système dans le cas inhomogène, c'est-à dire avec une densité variable. De plus, on s'intéresse au cas d'une densité de faible régularité qui est autorisée à présenter des discontinuités. Donc, le résultat que l'on démontre peut être mis en relation avec la dynamique des mélanges de nématiques non miscibles. On démontre l'existence globale en temps de solutions faibles de régularité invariante par changement d'échelle, en supposant une condition de petitesse sur les données initiales dans des espaces de Besov critiques. On démontre aussi l'unicité de ces solutions si de plus on suppose une condition supplémentaire de régularité pour les données initiales. Le système Beris-Edwards est analysé dans le cas bidimensionnel. On obtient l'existence et l'unicité de solutions faibles globales en temps, lorsque les données initiales sont dans des espaces de Sobolev spécifiques (sans condition de petitesse). Le niveau de régularité de ces espaces fonctionnels est adapté pour bien définir les solutions faibles. L'unicité est une question délicate et demande une estimation doublement logarithmique pour une norme sur la différence entre deux solutions dans un espace de Banach convenable. Le lemme d'Osgood permet alors de conclure à l'unicité de la solution. On obtient également un résultat de propagation de régularité d'indice positif. Afin de prendre en compte l'inertie des molécules, on considère aussi le modèle proposé par Qian et Sheng, et on étudie le cas de la dimension supérieure ou égale à deux. Ce système montre une caractéristique structurale spécifique, plus précisément la présence d'un terme inertiel, ce qui génère des difficultés significatives. On démontre l'existence d'une fonctionnelle de Lyapunov et l'existence et l'unicité de solutions classiques globales en temps, en considérant des données initiales petites. Enfin, on analyse le système de Boussinesq et on montre l'existence et l'unicité de solutions globales en temps. On considère la viscosité en fonction de la température en supposant simplement que la température initiale soit bornée, tandis que la vitesse initiale est dans des espaces de Besov avec indice de régularité critique. Les données initiales ont une composante verticale grande et satisfont à une condition de petitesse spécifique sur les composantes horizontales: elles doivent être exponentiellement petites par rapport à la composante verticale. / The present thesis is devoted to the dynamics of specific complex fluids. On the one hand we studythe dynamics of the so-called nematic liquid crystals, through the models proposed by Ericksen and Leslie, Beris and Edwards, Qian and Sheng.On the other hand we analyze the dynamics of a temperature-dependent complex fluid, whose dynamics is governed by the Boussinesq system.Nematic liquid crystals are materials exhibiting a state of matter between an ordinary fluid and a solid. In this thesis we are interested in studying the Cauchy problem associated to eachsystem modelling their hydrodynamics. At first, we establish some well-posedness results, such asexistence and uniqueness of global-in-time weak or classical solutions. Moreover we also analyzesome dynamical behaviours of these solutions, such as propagations of both higher and lowerregularities.The general framework for the initial data is that of Besov spaces, which extend the most widelyknown classes of Sobolev and Hölder spaces.The Ericksen-Leslie system is studied in a simplified form proposed by F. Lin and C. Liu,which retains the main difficulties of the original one. We consider both a two-dimensional and athree-dimensional space-domain. We assume the density to be no constant, i.e. the inhomogeneouscase, moreover we allow it to present discontinuities along an interface so that we can describe amixture of liquid crystal materials with different densities. We prove the existence of global-in-timeweak solutions under smallness conditions on the initial data in critical homogeneous Besov spaces.These solutions are invariant under the scaling behaviour of the system. We also show that theuniqueness holds under a tiny extra-regularity for the initial data.The Beris-Edwards system is analyzed in a two-dimensional space-domain. We achieve existenceand uniqueness of global-in-time weak solutions when the initial data belongs to specific Sobolevspaces (without any smallness condition). The regularity of these functional spaces is suitable inorder to well define a weak solution. We achieve the uniqueness result through a specific analysis,controlling the norm of the difference between to weak solutions and performing a delicate doublelogarithmicestimate. Then, the uniqueness holds thanks to the Osgood lemma. We also achieve aresult about regularity propagation.The Qian-Sheng model is analyzed in a space-domain with dimension greater or equal than two.In this case, we emphasize some important characteristics of the system, especially the presence ofan inertial term, which generates significant difficulties. We perform the existence of a Lyapunovfunctional and the existence and uniqueness of classical solutions under a smallness condition forthe initial data.Finally we deal with the well-posedness of the Boussinesq system. We prove the existence ofglobal-in-time weak solutions when the space-domain has a dimension greater or equal than two.We deal with the case of a viscosity dependent on the temperature. The initial temperature is justsupposed to be bounded, while the initial velocity belongs to some critical Besov Space. The initialdata have a large vertical component while the horizontal components fulfil a specific smallnessconditions: they are exponentially smaller than the vertical component.