Neste trabalho estudamos, no contexto de campo médio, modelos microscópicos que possam descrever o comportamento termodinâmico das fases nemáticas em sistemas líquido-cristalinos. Considerando apenas interações atrativas, investigamos modelos de interações quadrupolares para objetos intrinsecamente biaxiais. Esses modelos apresentam mesofases nemáticas uniaxiais e biaxiais, pontos triplos e multicríticos (tricríticos, pontos de Landau, etc.). Ainda no contexto de forças atrativas, introduzimos um modelo de mistura binária de objetos intrinsecamente uniaxiais e objetos intrinsecamente biaxiais, numa formulação annealed. Essa mistura apresenta diagramas de fases bastante ricos, com topologias diversas, onde identificamos estruturas uniaxiais e biaxiais, fases reentrantes e uma grande variedade de pontos multicríticos (tricríticos, pontos críticos terminais, etc.). No caso de interações estéricas, estudamos uma teoria do funcional densidade para sistemas anisotrópicos densos, construída a partir de uma aproximação de van der Waals. Para esferoides prolatos, o modelo prevê um espaço de orientações com regiões não-acessíveis para as partículas. Além disso, o sistema apresenta uma região de coexistência entre as fases nemática e isotrópica. / We study, in a mean-field approximation, microscopic models which can lead to nematic liquid-crystalline phases. Considering attractive forces, we investigate models with quadrupolar interactions for intrinsically biaxial objects. These models present uniaxial and biaxial nematic mesophases, triple and multicritical points (tricritical point, Landau point, etc.). We also introduce a model for a binary mixture of intrinsically uniaxiail and biaxial objects, in an annealed treatment. The mixture exhibits phase diagrams with very rich topologies, where we find uniaxial and biaxial structures, reentrant phases and many different multicritical behaviors (tricritical point, critical endpoint, etc.). Moreover, assuming steric interactions, we investigate a density functional theory for hard anisotropic bodies at high densities, based on a van der Waals approximation. For hard spheroids, the model leads to an orientation space with forbidden regions for the particles. Also, the system phase separates in a nematic and an isotropic phases.

Neste trabalho estudamos, no contexto de campo médio, modelos microscópicos que possam descrever o comportamento termodinâmico das fases nemáticas em sistemas líquido-cristalinos. Considerando apenas interações atrativas, investigamos modelos de interações quadrupolares para objetos intrinsecamente biaxiais. Esses modelos apresentam mesofases nemáticas uniaxiais e biaxiais, pontos triplos e multicríticos (tricríticos, pontos de Landau, etc.). Ainda no contexto de forças atrativas, introduzimos um modelo de mistura binária de objetos intrinsecamente uniaxiais e objetos intrinsecamente biaxiais, numa formulação annealed. Essa mistura apresenta diagramas de fases bastante ricos, com topologias diversas, onde identificamos estruturas uniaxiais e biaxiais, fases reentrantes e uma grande variedade de pontos multicríticos (tricríticos, pontos críticos terminais, etc.). No caso de interações estéricas, estudamos uma teoria do funcional densidade para sistemas anisotrópicos densos, construída a partir de uma aproximação de van der Waals. Para esferoides prolatos, o modelo prevê um espaço de orientações com regiões não-acessíveis para as partículas. Além disso, o sistema apresenta uma região de coexistência entre as fases nemática e isotrópica. / We study, in a mean-field approximation, microscopic models which can lead to nematic liquid-crystalline phases. Considering attractive forces, we investigate models with quadrupolar interactions for intrinsically biaxial objects. These models present uniaxial and biaxial nematic mesophases, triple and multicritical points (tricritical point, Landau point, etc.). We also introduce a model for a binary mixture of intrinsically uniaxiail and biaxial objects, in an annealed treatment. The mixture exhibits phase diagrams with very rich topologies, where we find uniaxial and biaxial structures, reentrant phases and many different multicritical behaviors (tricritical point, critical endpoint, etc.). Moreover, assuming steric interactions, we investigate a density functional theory for hard anisotropic bodies at high densities, based on a van der Waals approximation. For hard spheroids, the model leads to an orientation space with forbidden regions for the particles. Also, the system phase separates in a nematic and an isotropic phases.

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work. / Graduate