Two Dimensional Liquid Crystal Devices And Their Computer Simulations

Author : Obeng A. Addai
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Download or read book Mathematical Modeling Of Dye-Doped Liquid Crystal Devices And Computer Simulations Of Systems Of Repulsive Rod-Like Particles In 2D written by Obeng A. Addai and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guest-host liquid crystal (LC) devices rely on controlling the orientation of dichroic dyes dissolved in an LC host. Controlling the orientation of the liquid crystal and of the dissolved dye with an electric field allows control of the transmittance of the devices. Knowing the dielectric properties of the dye and liquid crystal mixtures at optical frequencies is crucial for the optimal design of guest-host liquid crystal devices. The dielectric functions of various layers in liquid crystal cells can be described by models imposing the Kramers-Kronig relations: the Sellmeier equation for transparent layers and causal Gaussian oscillator model for absorbing layers. We propose a systematic way to accurately model the dielectric response of each LC cell layer by minimizing the sum of squared differences between the measured transmittance spectrum of a guest-host cell in the near-UV/vis range and the prediction of the transmittance of the modeled multilayer structure. By measuring the transmittance for incident light polarized parallel and perpendicular to the nematic director allows us to separately characterize the two principal dielectric functions of the uniaxial sample. Our results show that the combined Sellmeier and causal Gaussian oscillator model can accurately characterize the dielectric functions of dyes and liquid crystals. In a dye-doped cholesteric LC in a planar state, the light maybe strongly absorbed and the transmittance maybe low. If the liquid crystal has positive dielectric anisotropy, the presence of an electric field, along the helical axis, unwinds the helix increasing the transmittance. To study the electric field effect on the light transmittance through such a guest-host device, we model the director field of the cholesteric LC between two parallel substrates with the one-dimensional Oseen- Frank theory. The surface anchoring energy has an additional term specifically for chiral systems. We study the dependencies of the electric-field-induced Freedericksz transition on the ratio of cell gap thickness to cholesteric pitch, d/P , and anchoring parameters. We show that the threshold voltage increases with d/P . The nature of the transition varies from continuous supercritical to discontinuous subcritical as d/P increases or as anchoring strength along the easy axis weakens. For large d/P , at the threshold voltage, the planar helical structure untwists and total angle of rotation of the director about the helical axis decreases by 2pi. Also, we show that the co-polarized and cross-polarized transmittance and reflectance of such a dye-doped cholesteric LC cell depend sensitively on wavelength and d/P , since the plane-polarized light becomes elliptically polarized after it propagates through a cholesteric LC cell. It is well-known that rod-like molecules interacting via long-range attractive interactions or short-range repulsive potentials can exhibit orientational order. We are interested in what would happen to systems of rod-like particles in a plane interacting via long-range repulsive potential. In our model, each particle consists of a number of point dipoles uniformly distributed along the particle length, with all dipoles pointing along the z-axis, so that the rod-like particles repel each other when they lie in the x-y plane. Dipoles from different particles interact via an r^3 potential, where r is the distance between the dipoles. We have considered two model systems, each with N particles in a unit cell with periodic boundary conditions. In the first, particle centers are fixed on a square or triangular lattice but they are free to rotate. In the second, particles are free to translate as well as in cells with variable shapes. Here they self-assemble to form configurations where the stress tensors are isotropic. Our numerical results show that at low temperatures the particles tend to form stripes with alternating orientations, resembling herringbone patterns or the anticlinic SmCA LC phase.