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Dans cette thèse, nous nous sommes intéressés initialement aux transitions de phase qui ont lieu dans les cristaux liquides (CL), d'un point de vue théorique et numérique. En effet, les résultats présentés ici découlent de simulations numériques Monte Carlo (MC) et de développements analytiques basés sur des modèles de physique statistique et de matière condensée. Une forte analogie existe entre les systèmes de spins et les CL.Par exemples, ces derniers présentent des phases où les molécules sont toutes alignées dans le même sens comparables aux spins dans les matériaux ferromagnétiques. D'autres phases, dites cholesteriques, sont caractérisées par un arrangement moléculaire ressemblant beaucoup aux structures helimagnétiques. Mais les CL étant un état de la matière intermédiaire, situé entre le solide et le liquide, il est nécessaire de tenir compte des mouvements des molécules dans les modèles et d'adapter en conséquence l'algorithme de MC utilisé.Après une courte introduction sur les CL et leurs applications dans le premier chapitre, le second chapitre est longuement dédié aux méthodes MC et à l'adaptation de l'algorithme de Metropolis-Hastings afin d'introduire la mobilité des molécules.Le chapitre III est en quelque sorte un cas test pour simuler les CL. On considère un ensemble de molécules sur réseau et dont le nombre est inférieur au nombre de sites du réseau. L'interaction entre spins de plus proches voisins est de type Potts. L'état de plus basse énergie correspond au cas où tous les spins sont tassés au fond de la cuve.Ce système est d'abord traité par une étude de champ moyen dont les résultats sont confirmés par les simulations. Il apparaît que les couches de surface subissent une fusion et que le cœur du solide restant subit une transition du premier ordre.Le quatrième chapitre est consacré à des structures topologiques particulières que sont les skyrmions et des structures en bandes que l'on peut trouver dans les CL. A l'aide d'interactions Dzyaloszhinski-Moria (DM) D en présence d'une interaction d'échange J dans des films minces, nous étudions dans un premier temps les excitations des ondes de spin, également appelées magnons, qui sont le résultat d'une excitation collective de spins. Grâce aux fonctions de Green, nous calculons le spectre d'ondes de spin permettant ainsi de déterminer les propriétés à T = 0 et à température finie. Dans un deuxième temps, nous appliquons un champ magnétique H orthogonal au film mince faisant apparaître un cristal de skyrmions. En utilisant des simulations MC, nous montrons des vortex pour lesquels chaque centre peut être considéré comme le nœud d'une super-structure. Nous parlons alors de cristal de skyrmions. Selon les valeurs de D/H les simulations peuvent montrer également une structure semblable à celle que l'on trouve dans certains CL.Le chapitre suivant est consacré à l'étude de la dynamique conduisant à la formation des phases nématique et smectique à l'aide d'un modèle mobile de Potts. Nous observons ici les mécanismes qui se produisent pour former un cristal liquide nématique ou smectique lors du refroidissement à partir d'une phase isotrope. Le choix des interactions est crucial pour modéliser ces deux phases.Dans le chapitre VI, nous traitons de l'interaction dipolaire dans les nano dots avec un modèle de spin d'Heisenberg. La première partie du chapitre est consacrée à l'état fondamental présentant un vortex autour du centre du dott. Les spins sont coplanaires au plan du dot sauf à proximité du centre du dot où ils ont une composante z non nulle. Nous étudions ensuite l'effet de la température et la fusion du dot. La température de fusion du dot ne dépend pas de la taille du système, ce qui est très différent de ce qui se passe dans le cas des spins localisés. Ce chapitre n'est pas directement lié aux CL, mais est le premier pas dans la construction d'un modèle plus complet pour décrire le mécanisme conduisant aux phases cholestériques. / In this thesis, we are initially interested in the phase transitions that take place in liquid crystals (LC), from a theoretical and numerical point of view. Indeed, the results presented here are derived from Monte Carlo (MC) simulations and analytical developments based on statistical physics and condensed matter models. A strong analogy exists between spin systems and LC. For example, the latter have phases where the molecules are all aligned in the same direction (orientational order) comparable to spins in ferromagnetic materials. Other phases, called cholesteric, are characterized by a molecular arrangement very similar to the helimagnetic structures. But LC being an intermediate state of matter, between the solid and the liquid phase, it is necessary to take into account the motions of the molecules in the models and to adapt accordingly the MC algorithm.After a short and general introduction on LC and their applications in the first chapter, the second chapter is devoted to MC methods and the adaptation of the Metropolis-Hastings algorithm in order to introduce the mobility of molecules in our systems.Chapter III is a test case to simulate LC. We consider a set of molecules on a lattice. The number of molecules is smaller than the number of the lattice sites to allow for a molecule mobility between sites. The interaction between nearest neighbouring spins is supposed to be a Potts model. The lowest energy state corresponds to the case where all the spins are packed at the bottom of the tank. This solid ground state becomes a liquid at high temperatures.This system is first treated with a mean-field analysis whose results are confirmed by the MC simulations. It appears that the surface layers undergo a melting and that the core of the remaining solid undergoes a first-order phase transition.The following chapter is devoted to particularly topological structures which are skyrmions and stripe structures. These structures are often observed in LC. We use a Dzyaloshinski-Moria (DM) interaction of strength D in addition to an exchange interaction J to study properties of thin films. In a first part of the chapter, we study the spin-wave excitations, also termed magnons, that are the result of a collective excitation of spins. Using the Green's function, we calculate the spin-wave spectrum which is used next to determine properties at T=0 and at finite temperatures. In the second part of the chapter, we apply a magnetic field H orthogonal to the thin film making appear a crystal of skyrmions. Using MC simulations, we show that skyrmions arranged on a super-structure of a triangular geometry. Depending on the value of D/H, these simulations also show a labyrinth-like structure very close to the filament-shaped structures found in certain LC.The next chapter is devoted to the study of the dynamics leading to the formation of the nematic and smectic phases using a mobile Potts model. We observe here how the nematic and smectic LC are dynamically formed upon cooling from the isotropic phase. The choice of the interactions is crucial to model these two phases.In the chapter VI, we deal with the dipolar interaction in nanodots using the Heisenberg spin model. The first part of the chapter is devoted to the determination of the ground state exhibiting a vortex around the center of the dot. The spins lie in the xy plane at the border of the dot but go out of the xy plane at the dot center to give rise to a non-zero z component. We then study the effect of the temperature and the melting of the dot. The melting temperature of the dot do not depend on the size of the system. This is very different with the case of localised spins where the transition temperature increases with increasing the film thickness. This chapter is not directly related to LC. It was the first step towards a more complicated model describing the mechanism leading to cholesteric LC phases.

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Proper design of high performance industrial heat transfer equipment relies on accurate knowledge and prediction of the thermal boundary conditions. In order to enhance the overall gas turbine efficiency, advancements in cooling technology for gas turbines and related applications are continuously investigated to increase the turbine inlet temperature without compromising the durability of the materials used. For detailed design, local distributions are needed in addition to bulk quantities. Detailed local distributions require advanced experimental techniques whereas they are readily available using numerical tools. Numerical predictions using a computational fluid dynamics approach with popular turbulence models are benchmarked against a semi-empirical correlation for the friction in a circular channel with repeated-rib roughness to demonstrate some shortcomings of the models used. Numerical predictions varied widely depending on the turbulence modelling approach used. The need for a compatible experimental dataset to accompany numerical simulations was discussed. An exact, closed-form analytical solution to the enhanced lumped capacitance model is derived. The temperature evolution in a representative 2D turbulated surface is simulated using Fluent to validate the model and its exact solution. A case including an interface contact resistance was included as well as various rib sizes to test the validity of the model over a range of conditions. The analysis was extended to the inter-rib region to investigate the extent and magnitude of the influence of the metallic rib features on the apparent heat transfer coefficients in the inter-rib region. It was found that the thermal contamination is limited only to the regions closest to the base of the rib feature. An experimental setup was developed, capable of measuring the local heat transfer distributions on all four channel walls of a rectangular channel (with aspect ratios between 1 and 5) at Reynolds numbers up to 150,000. The setup utilizes a transient thermochromic liquid crystals technique using narrow band crystals and a four camera setup. The setup is used to test a square channel with ribs applied to one wall. Using the transient thermochromic liquid crystals technique and applying it underneath high conductivity, metallic surface features, it is possible to calculate the heat transfer coefficient using a lumped heat capacitance approach. The enhanced lumped capacitance model is used to account for heat conduction into the substrate material. Rohacell and aluminum ribs adhered to the surface were used to tandem to validate the hybrid technique against the standard technique. Local data was also used to investigate the effect of thermal contamination. Thermal contamination observed empirically was more optimistic than numerical predictions. Traditional transient thermochromic liquid crystals technique utilizes the time-to-arrival of the peak intensity of the green color signal. The technique has been extended to utilize both the red and green color signals, increasing the throughput by recovering unused data while also allowing for a reduction in the experimental uncertainty of the calculated heat transfer coefficient. The over-determined system was solved using an un-weighted least squares approach. Uncertainty analysis of the multi-color technique demonstrated its superior performance over the single-color technique. The multi-color technique has the advantage of improved experimental uncertainty while being easy to implement.

Water soluble conjugated polyelectrolytes (CPEs), which fall under the category of conductive polymers, possess numerous advantages over other conductive materials for the fabrication of electronic devices. Namely, the processing of water soluble conjugated polyelectrolytes into thin film electronic devices is much less costly as compared to the processing of inorganic materials. Moreover, the handling of conjugated polyelectrolytes can be performed in a much more environmentally friendly manner than in the processing of other conjugated polymers because conjugated polyelectrolytes are water soluble, whereas other polymers will only dissolve in toxic organic solvents. The processing of electronic devices containing inorganic constituents such as copper indium gallium selenide (CIGS), is much more expensive and poses much greater environmental risks because toxic metals may be released into landfills or waterways upon cell disposal.75 Because conjugated polyelectrolytes enjoy an assortment of advantages over other materials for the manufacturing of thin film electronic devices, there is globally vested interest in the researching of their properties. Despite the fact that CPEs can serve as efficient electron transport mediums, devices such as organic solar cells cannot realize their highest efficiencies unless the morphology of CPEs is precisely controlled. Charged surfactants can electrostatically and ionically interact with CPEs, and when introduced in specific concentrations, molar ratios, and temperature ranges, will aid in a ‘coil to rod’ transition of the CPE, wherein polymer chains undergo intramolecular transitions to obtain rigid-rod morphologies. The kinetics and thermodynamics of the ‘coil to rod’ transition are heavily dependent upon the type(s) of charged surfactant complexed with the CPE (i.e. on the surfactant architecture). By performing UV/Vis Spectroscopy and Fluorometry on dilute polymer/surfactant solutions, Polarized Optical Microscopy (POM) and Small Angle X-Ray Scattering (SAXS) on high concentration polymer/surfactant solutions, and Differential Scanning Calorimetry (DSC) and X-Ray Diffraction (XRD) on solid-state polymer/surfactant samples, the role of various surfactant architectures on the kinetics and thermodynamics of the ‘coil to rod’ transition was studied. The liquid crystalline physical properties and the extent of solid state crystallinity were also investigated. Through an analysis of the data obtained from these various techniques, it was found that the ‘coil to rod’ transition is progressively favored when the alkyl chain length of a single tailed surfactant is sequentially increased, and that as the concentration of double-tailed surfactant increases, the ‘coil to rod’ transition is negated.

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