We present a study of the theory and simulation of Liquid Crystals. A general introduction to the field is given, then the essential features of the Monte Carlo (MC) sampling algorithm are described and explained, along with some of the practical considerations in the implementation of MC. Several quantitative measures used to describe liquid crystalline systems are outlined, including the second rank order tensor, in addition to some of those from elastic theory and density functional theory. Monte Carlo Simulations were performed in bulk geometry in the canonical ensemble in order to calculate the Frank elastic constants of hard spherocylinders, hard platelets and hard cut-spheres at three thicknesses. Onsager’s density functional theory was also performed to yield the elastic constants for hard platelets, and this amounts to using a virial expansion in the free energy, truncated at second order. Our collaborators for O’Brien et al. [2008] provided results for the elastic constants from a calculation of the higher order virial coefficients. All of the results from theory are compared to simulation, with some experimental determinations available. All three elastic constants compared well with the high-order virial theory, there is quantitative agreement with the experimental values, and the effect of increasing thickness of discs was found to improve the agreement of the ratio of K1/K3. Aspects of translationally ordered phases are studied in the context of constrained non-equilibrium systems. Monte Carlo was also performed for platelets confined in wedge geometry, with several choices for the types of wall. A local approximation is utilised to yield the depletion force and potential as a function of the wall separation, as well as the adsorption between the walls. The adsorption for large separations exhibited general qualitative agreement with theory and Gibbs Ensemble simulations. The two different wall boundary conditions produced different orientational structural features, with repulsive and attractive depletion potentials measured, and a planar surface phase that does not appear in the bulk is categorised.

In this thesis we study the interactions between light and matter in photorefractive liquid crystal cells. To model the liquid crystal alignment we develop a fast and accurate approximation of the normally stiff equations which minimise the Landau-deGennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically, they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order (10−4) when compared to the full stiff equations. As this approximation is based on aQ–tensor formalism, the sign reversal symmetry of the liquid crystal is respected. We consider both the simplified case, where the director is restricted to a plane, and the full three-dimensional case. An approximation of the error is also given. We use the liquid crystal model to understand two different optical effects. The first of these is optical coupling. This effect is observed in liquid crystals in both the Bragg and Raman–Nath regimes. To account for this behaviour we develop an extension to the coupled wave theory which is suitable for all regimes of coupling. The model assumes that the refractive index grating, generated by the liquid crystal, has an arbitrary profile in one direction and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are considered and appropriate mismatch terms dealt with. It is shown that this model is analytically equivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate set of assumptions. This model is also verified through comparison to finite element simulations of Maxwell’s equations. The second effect we model is the coupling of surface plasmon polaritons at the interface between a metal layer and a photorefractive liquid crystal cell. We implement existing numerical models to gain a thorough understanding of the system. These models are qualitatively compared with experimental observations. Analytic approximations to describe the coupling of surface plasmon polaritons at the surface of the liquid crystal cell are developed. These expressions provide a great deal of insight into the coupling mechanisms and will be of fundamental importance in optimising these systems.

Many optical processing systems rely critically on the availability of high performance, electrically-addressed spatial light modulators. Ferroelectric liquid crystal over silicon is an attractive spatial light modulator technology because it combines two well matched technologies. Ferroelectric liquid crystal modulating materials exhibit fast switching times with low operating voltages, while very large scale silicon integrated circuits offer high-frequency, low power operation, and versatile functionality. This thesis describes the design and characterisation of the SBS256 - a general purpose 256 x 256 pixel ferroelectric liquid crystal over silicon spatial light modulator that incorporates a static-RAM latch and an exclusive-OR gate at each pixel. The static-RAM latch provides robust data storage under high read-beam intensities, while the exclusive-OR gate permits the liquid crystal layer to be fully and efficiently charge balanced. The SBS256 spatial light modulator operates in a binary mode. However, many applications, including helmet-mounted displays and optoelectronic implementations of artificial neural networks, require devices with some level of grey-scale capability. The 2 kHz frame rate of the device, permits temporal multiplexing to be used as a means of generating discrete grey-scale in real-time. A second integrated circuit design is also presented. This prototype neuraldetector backplane consists of a 4 x 4 array of optical-in, electronic-out processing units. These can sample the temporally multiplexed grey-scale generated by the SBS256. The neurons implement the post-synaptic summing and thresholding function, and can respond to both positive and negative activations - a requirement of many artificial neural network models.

The initial aim of the work presented in this thesis was to examine smectic layer compressibility with a view to improving our understanding of the stability of intermediate phases. A natural starting point was to investigate the smectic-A phase, as it is the most basic of the smectic phases. The response of the layered structure to external fields is also a focus of this thesis as electric and magnetic fields enable the layer properties to be probed. Investigations into the reorientation dynamics of smectic-A layers in magnetic fields were performed using geometries and cell thicknesses (>50 μm) that are not feasible using electric fields. Data presented in this thesis show that three distinct reorientation mechanisms can occur, one of which is previously unreported and bridges the gap between the previously known mechanisms. The new mechanism observed in 270 μm and 340 μm thickness cells exhibits multiple stage reorientation on a timescale between tens and hundreds of seconds. Using conventional electro-optic techniques combined with a theoretical approach developed by others, this thesis presents a new technique to provide measurement of relative smectic layer compressibility of eight smectic-A liquid crystalline materials. The method presented here combines data on cell thickness, dielectric anisotropy and the measurement of the voltage threshold of the toroidal to stripe domain transition. As expected, the experimental data indicated that materials with shorter molecular lengths had the largest relative layer compressibility. Finally, direct measurement of smectic layer compressibility was investigated and the design of an apparatus capable of such measurements was undertaken. Preliminary results from such an apparatus are presented along with a discussion on the steps taken to develop the design.

No description available.

Cette thèse a pour objectif de comprendre les mécanismes physiques régissant la formation de capsules submillimétriques à coeur aqueux possédant une membrane fine d'hydrogel et ainsi de mieux maitriser ce procédé. Des bigouttes sont d'abord formées dans l'air par fragmentation d'un jet cylindrique composé d'un coeur aqueux enveloppé par une solution d'alginate. La coque est ensuite gélifiée après immersion dans une solution de calcium. L'étude du co-Écoulement au sein de l'injecteur a montré l'existence d'une instabilité élastique qui est amplifiée en présence de cations, du fait du caractère polyélectrolyte de l'alginate. Nous avons montré que cette instabilité était à l'origine d'un battement du jet composé en sortie d'extrusion. En provoquant un décentrage du coeur, l'instabilité induit une relaxation asymétrique du profil de vitesse, ce qui crée un couple qui courbe le jet. Nous avons mis en évidence cet effet en produisant des jets courbés à partir d'une pointe biseautée. La fragmentation du jet est ensuite contrôlée par une perturbation harmonique des débits d'injection. Nous observons une décroissance de la vitesse d'onde à la surface du jet pilotée par la tension de surface. La viscosité élevée des solutions d'alginate entraine une amplification de fluctuations de cette vitesse donnant lieu à des coalescences au sein du jet. L'ajout de tensioactifs peut exacerber cet effet en induisant une tension de surface dynamique à la surface du jet. Finalement, nous parvenons à produire des capsules submillimétriques de taille contrôlée, monodisperses, possédant une membrane fine, avec un taux d'encapsulation supérieur à 99%. Ces capsules trouvent des applications dans le domaine des biotechnologies comme nouvel outil pour la culture cellulaire. / The purpose of this work is to understand physical mechanisms that control the formation of aqueous-Core submillimetric capsules with a thin hydrogel membrane. This comprehension will allow a better control of the process. Compound drops are first formed in the air by the break-Up of a cylindrical jet composed of an aqueous core surrounded by an alginate solution. The shell is then solidified after immersion in a gelling calcium solution. The study of the co-Flow inside the injector showed the existence of an elastic instability which is amplified in the presence of cations, due to the polyelectrolyte property of alginate. We showed that this instability causes the flapping of the compound jet out of the injector. The instability induces a displacement of the core fluid position which leads to an asymmetric velocity relaxation that creates a torque and finally bends the jet. We produced curved jets with a beveled capillary to demonstrate this effect. The jet break-Up is controlled by a harmonic perturbation of the injection flow rates. We measured a decrease of the wave speed on the jet surface which is controlled by the surface tension. The alginate solution high viscosity causes an amplification of speed fluctuations that induces coalescence inside the jet. This amplification is enhanced by the addition of surfactants which create a dynamic surface tension at the jet interface. Finally, we managed to produce submillimetric and monodisperse capsules with a thin membrane, an encapsulation yield above 99% and a size that we can tune. These capsules can be used in biotechnology applications as a new tool for cell culture.

Highly correlated electron materials are systems in which many new states of matter can emerge. A particular situation which favours the formation of exotic phases of the electron liquid in complex materials is that where a quantum critical point (QCP) is present in the phase diagram. Neighbouring regions in parameter space reveal unusual physical properties, described as non-Fermi liquid behaviour. One of the important problems in quantum criticality is to find out how the Fermi surface (FS) of a material evolves near a QCP. The traditional method for studying the FS of materials is the de Haas van Alphen effect (dHvA). A quantum critical end point (QCEP) has been reported in the highly correlated metal Sr₃Ru₂O₇, which is tuned using a magnetic field high enough to perform the dHvA experiment. It moreover features a new emergent phase in the vicinity of the QCEP, a nematic type of electron ordering. The subject of this thesis is the study of the FS of Sr₃Ru₂O₇ using the dHvA effect. Three aspects were explored. The first was the determination of the FS at fields both above and below that where the QCEP arises. The second was the search for quantum oscillations inside the nematic phase. The third was a reinvestigation of the behaviour of the quasiparticle effective masses near the FS. In collaboration with angle resolved photoemission spectroscopy experimentalists, a complete robust model for the FS of Sr₃Ru₂O₇ at zero fields was determined. Moreover, the new measurements of the quasiparticle masses revealed that no mass enhancements exist anywhere around the QCEP, in contradiction with previous specific heat data and measurements of the A coefficient of the power law of the resistivity. Finally, we report dHvA oscillations inside the nematic phase, and the temperature dependence of their amplitude suggests strongly that the carriers consist of Landau quasiparticles.

Ce travail de thèse expérimental porte sur les dynamiques d'imbibition en milieu confiné. Cette situation survient lorsqu'un fluide mouillant les parois d'un solide vient déplacer un second fluide non-miscible. La divergence des contraintes visqueuses au niveau de la ligne de contact avec le solide complexifie la description de la forme et de la dynamique d'invasion du ménisque qui ne peut se résumer, même aux échelles macroscopique du confinement solide, à l'avancement d'un front liquide homogène. L'absence de longueur caractéristique intrinsèque aux fluides nécessite de tenir compte des couplages entre écoulement et forme des interfaces à toutes les échelles, depuis le nanomètre (interactions moléculaires) jusqu'à l'échelle du confinement (une centaine de micromètres dans nos expériences). Ce caractère multi-échelle est au centre des travaux effectués durant cette thèse. A l'aide du développement de nouveaux outils microfluidiques, nous étudions quantitativement l'imbibition dans une géométrie de type Hele-Shaw. Une étude à la fois expérimentale et numérique nous permet de mettre en évidence l'existence d'une nouvelle transition d'entrainement. Une étude complète du modèle numérique nous permet ensuite d'unifier ce nouveau mode avec celui reporté jusqu'à présent dans la littérature. Nous nous intéressons aussi à l'imbibition dans des réseaux poreux modèle. Nous identifions alors expérimentalement un nouveau mode d'invasion généralisant l'entrainement obtenu précédemment. Ce scénario est piloté par l'écoulement en film de coin autour des obstacles constituant le poreux. Nous proposons alors un critère géométrique simple pour discriminer les différents modes d'invasions. / This experimental thesis deals with imbibition in confined media. This situation occurs when a fluid which preferentially wets the solid displaces another immiscible fluid. The divergence of the viscous stress at the contact line with the solid complicates the description of both the shape and the invasion dynamic of the meniscus that can no longer be described, even at the macroscopic length scale of the solid confinement, by only the displacement of a homogeneous liquid front. The absence of any intrinsic fluids length scale requires to take into account the coupling between the interface shape and the flow at all scales, from nanometers (molecular interaction) to solid confinement scale (hundred micrometers in our experiments). Multi-scale behavior will be the central point of this thesis. Using new microfluidics tools, we first made a quantitative study of imbibitions in Hele-Shaw geometry. We demonstrate a new class of liquid entrainment transition both experimentally and numerically. In addition, an extensive analysis of our numerical model shows that it consistently describes all scenarios that have been reported so far. We then study imbibitions in model porous media. We demonstrate a new invasion process, where the flow occurs along the corner of the porous? obstacles, that generalizes the previous entrainment. We finally propose a geometric criterion that discriminates between the different invasion scenarios.

The structure of molten Au0.81Si0.19, Au0.72Ge0.28 and Ag0.74Ge0.26 alloys with a composition at or near to the eutectic was investigated by using neutron diffraction (ND). The results suggest that the Au-Au distance in the alloys is similar to that of liquid Au, there is a preference for Au-Si bonds and show that there are pre-peaks in the total structure factors for Au0.72Ge0.28 and Ag0.74Ge0.26 at 1.3(2) and 1.6(3) ˚, A−1 respectively. The asymptotic decay of the pair correlation functions was found to agree both with a theoretical prediction based on simple pair potentials and a fractal model for metallic glasses. The structure of glassy (R2O3)0.2(Al2O3)0.2(SiO2)0.6, where R denotes Dy, Ho or a 50:50 mixture of Dy and Ho, was investigated by using the method of isomorphic substitution in ND, x-ray diffraction (XRD) and extended x-ray absorption fine structure (EXAFS) spectroscopy. The network is made from SiO4 tetrahedral units with a distribution of AlO4, AlO5 and AlO6 units giving an average coordination number of 4.5(1). There is a distribution of RO5, RO6, RO7, RO8 and RO9 units with an average coordination number of 7.2(3) and an average R-O distance of 2.33(2) ˚ A. The EXAFS results confirmed that Dy and Ho are isomorphic and were used to refine an RMC model of the structure. R-Al and R-Si nearest neighbour shells with average distances of 3.15(3) and 3.6(1) ˚A were required to fit the EXAFS results. The structure of glassy and liquid ZnCl2 was studied by using ND and XRD. The material has a network structure made from ZnCl4 tetrahedra units which is retained in the liquid at temperatures near to the boiling point. An increase of temperature promotes edge sharing connectivity as inferred from a decrease of the Zn-Zn nearest neighbour distance and average Zn-Cl coordination number. An EXAFS study on crystalline ZnCl2 at room temperature shows that Zn remains 4fold coordinated at pressures less than 1 GPa, is 4+2-fold coordinated at 2-4 GPa, and is 6-fold coordinated above 4 GPa. For liquid ZnCl2, Zn is 4-fold coordinated by Cl at a pressure of about 1 GPa and could be 6-fold coordinated at 2-3 GPa.

No description available.