Erms Pereira

Principles of thermal design with nematic liquid crystals

Highly engineered materials are arousing great interest because of their ability to manipulate heat, as described by the coordinate transformation approach. Based on recently developed analog gravity models, we present how a simple device based on nematic liquid crystals can achieve in principle either thermal concentration or expulsion. These outcomes are shown to stem from the topological properties of a disclination-like structure, induced in the nematic phase by anchoring conditions.

Metric approach for sound propagation in nematic liquid crystals

In the eikonal approach, we describe sound propagation near topological defects of nematic liquid crystals as geodesics of a non-Euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermats principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve information about the elastic constants.

Diffraction of light by topological defects in liquid crystals

Light scattering due to hedgehog-like and linear disclination topological defects in a nematic liquid crystal has been studied. Light propagation close to such defects appears to be a metric equivalent to the spatial element of the global monopole and cosmic string geometries. Using a metric approach, the amplitude of the scattering and the differential and total scattering cross section have been obtained for the hedgehog defect in terms of the characteristic parameters of a liquid crystal. In the case of disclination, a cylindrical partial wave method has been developed. Applying the results of earlier studies, we have also examined the influence of temperature on the localisation of the diffraction patterns.

Thermal diode made by nematic liquid crystal

Abstract This work investigates how a thermal diode can be designed from a nematic liquid crystal confined inside a cylindrical capillary. In the case of homeotropic anchoring, a defect structure called escaped radial disclination arises. The asymmetry of such structure causes thermal rectification rates up to 3.5% at room temperature, comparable to thermal diodes made from carbon nanotubes. Sensitivity of the system with respect to the heat power supply, the geometry of the capillary tube and the molecular anchoring angle is also discussed.

Optics near a hyperbolic defect

We examine the properties of a family of defects called hyperbolic disclinations, and discuss their possible use for the design of perfect optical absorbers. In hyperbolic metamaterials, the ratio of ordinary and extraordinary permittivities is negative, which leads to an effective metric of Kleinian signature (two timelike coordinates). Considering a disclination in the hyperbolic nematic host matrix, we show that the timelike geodesics are Poinsot spirals, i.e., whatever the impact parameter of an incident light beam, it is confined and whirls about the defect core. The trapping effect does not require light to be coherent. This property also remains in the wave formalism, which may be the sign for many potential applications.

Generation of optical vorticity from topological defects

The propagation of an electromagnetic wave along a chiral string (or screw dislocation) is studied. Adopting the formalism of differential forms, it is shown that the singular torsion of the defect is responsible for quantized modes. Moreover, it is demonstrated that the modes thus obtained have well defined orbital angular momentum, opening the possibility for applications relevant both for cosmology and for optics.

Flowing liquid crystal simulating the Schwarzschild metric

We show how to simulate the equatorial section of the Schwarzschild metric through a flowing liquid crystal in its nematic phase. Inside a liquid crystal in the nematic phase, a traveling light ray feels an effective metric, whose properties are linked to perpendicular and parallel refractive indexes, no and ne respectively, of the rod-like molecule of the liquid crystal. As these indexes depend on the scalar order parameter of the liquid crystal, the Beris-Edwards hydrodynamic theory is used to connect the order parameter with the velocity of a liquid crystal flow at each point. This way we calculate a radial velocity profile that simulates the equatorial section of the Schwarzschild metric, in the region outside of Schwarzschild’s radius, in the nematic phase of the liquid crystal. In our model, the higher flow velocity can be on the order of some meters per second.

Geometrical optics limit of phonon transport in a channel of disclinations

Abstract The presence of topological defects in a material can modify its electrical, acoustic or thermal properties. However, when a group of defects is present, the calculations can become quite cumbersome due to the differential equations that can emerge from the modeling. In this work, we express phonons as geodesics of a 2 + 1 spacetime in the presence of a channel of dislocation dipoles in a crystalline environment described analytically in the continuum limit with differential geometry methods. We show that such a simple model of 1D array of topological defects is able to guide phonon waves. The presence of defects indeed distorts the effective metric of the material, leading to an anisotropic landscape of refraction index which curves the path followed by phonons, with focusing/defocusing properties depending on the angle of the incident wave. As a consequence, using Boltzmann transfer equation, we show that the defects may induce an enhancement or a depletion of the elastic energy transport. We comment on the possibility of designing artificial materials through the presence of topological defects. We show that a simple model of 1D array of topological defects in a crystalline environment is able to guide acoustic waves, depending on the angle of the incident wave. We comment on a recently proposed geophysical mechanism explaining the mantle dynamics by the presence, in some crystalline materials there, of wedge disclinations.

Retrieving the saddle-splay elastic constant K24 of nematic liquid crystals from an algebraic approach

Abstract.The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K24. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a 2 H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K24. Considering an escaped-radial disclination inside a capillary tube with radius R0 of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle

Concurrent guiding of light and heat by transformation optics and transformation thermodynamics via soft matter

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