Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.

Nematic wetting and filling of crenellated surfaces

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau-de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.

Qualidade de vida das famílias de crianças com surdez: avaliação na perspectiva das famílias

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Ciências da Educação - Especialidade Educação Especial

Qualidade de vida das famílias apoiadas por intervenção precoce: identificação de fatores mais valorizados pelas famílias

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Intervenção Precoce

Biaxial Nematic Order in the Hard-boomerang Fluid

We consider a fluid of hard boomerangs, each composed of two hard spherocylinders joined at their ends at an angle Psi. The resulting particle is nonconvex and biaxial. The occurence of nematic order in such a system has been investigated using Straley's theory, which is a simplificaton of Onsager's second-virial treatment of long hard rods, and by bifurcation analysis. The excluded volume of two hard boomerangs has been approximated by the sum of excluded volumes of pairs of constituent spherocylinders, and the angle-dependent second-virial coefficient has been replaced by a low-order interpolating function. At the so-called Landau point, Psi(Landau)approximate to 107.4 degrees, the fluid undergoes a continuous transition from the isotropic to a biaxial nematic (B) phase. For Psi not equal Psi(Landau) ordering is via a first-order transition into a rod-like uniaxial nematic phase (N(+)) if Psi > Psi(Landau), or a plate-like uniaxial nematic (N(-)) phase if Psi < Psi(Landau). The B phase is separated from the N(+) and N(-) phases by two lines of continuous transitions meeting at the Landau point. This topology of the phase diagram is in agreement with previous studies of spheroplatelets and biaxial ellipsoids. We have checked the accuracy of our theory by performing numerical calculations of the angle-dependent second virial coefficient, which yields Psi(Landau)approximate to 110 degrees for very long rods, and Psi(Landau)approximate to 90 degrees for short rods. In the latter case, the I-N transitions occur at unphysically high packing fractions, reflecting the inappropriateness of the second-virial approximation in this limit.

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nernatic is investigated i) analytically using the tenser order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nernatic director changes from oblique to perpendicular.

Desenvolvimento de modelo de primeiros princípios para simulação dinâmica de uma coluna de destilação contínua

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Química e Biológica

Liquid-vapor interfaces of patchy colloids

We investigate the liquid-vapor interface of a model of patchy colloids. This model consists of hard spheres decorated with short-ranged attractive sites ("patches") of different types on their surfaces. We focus on a one-component fluid with two patches of type A and nine patches of type B (2A9B colloids), which has been found to exhibit reentrant liquid-vapor coexistence curves and very low-density liquid phases. We have used the density-functional theory form of Wertheim's first-order perturbation theory of association, as implemented by Yu and Wu [J. Chem. Phys. 116, 7094 (2002)], to calculate the surface tension, and the density and degree of association profiles, at the liquid-vapor interface of our model. In reentrant systems, where AB bonds dominate, an unusual thickening of the interface is observed at low temperatures. Furthermore, the surface tension versus temperature curve reaches a maximum, in agreement with Bernardino and Telo da Gama's mesoscopic Landau-Safran theory [Phys. Rev. Lett. 109, 116103 (2012)]. If BB attractions are also present, competition between AB and BB bonds gradually restores the monotonic temperature dependence of the surface tension. Lastly, the interface is "hairy," i.e., it contains a region where the average chain length is close to that in the bulk liquid, but where the density is that of the vapor. Sufficiently strong BB attractions remove these features, and the system reverts to the behavior seen in atomic fluids.

Preserving the validity of the two-Higgs-doublet model up to the Planck scale

We examine the constraints on the two Higgs doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor changing neutral currents. Using basis independent techniques, we exhibit robust regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.