Numerical investigation of director orientation and flow of nematic liquid crystals in a planar 1:4 expansion

Cruz, Pedro Alexandre da; Tomé, Murilo Francisco; Stewart, Iain W.; McKee, Sean

doi:10.2140/jomms.2011.6.1017

Cited by 2 publications

(3 citation statements)

References 24 publications

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“…On the other hand, is given by: (2) following the Maxwell equations: (3) where the dielectric tensor for a nematic LC is: (4) is the dielectric anisotropy and the ordinary permittivity. The Gibbs free energy (WG), given by the integral of the free energy density over the thickness, has a minimum in the equilibrium state.…”

Section: Solving Continuum Theorymentioning

confidence: 99%

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Modeling electro-optical response of nematic liquid crystals by numerical methods

Algorri¹

2013

Opt. Pura Apl.

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ABSTRACT:In this study, a novel algorithm to solve the position of a nematic liquid crystal molecular director inside a device has been proposed. The formulation for minimizing the Gibbs free energy, composed by the free energy deformation (Frank-Oseen equations) minus the electrical energy, has been established using a vectorial representation of the director. The three liquid crystal elastic constants have been considered. The differential equations involved have been solved by applying numerical methods, using an algorithm developed by the authors. It has been compared with other techniques and the main advantages are that the new algorithm is faster and more accurate than other previous methods such as finite difference method (FDT) or a boundary value problem solver of MATLAB (bvp4c). Simulation program is also a powerful tool for analyzing other liquid crystal properties such as refractive index and permittivity as a function of voltage. To validate the simulation results, they have been compared with some measurements of a nematic liquid crystal device manufactured for that purpose. The comparison of birefringences simulated and measured show results that are fairly in agreement. This work also aims to provide a software simulation tool easy to reprogram for more complex devices.Key words: Optoelectronics; Liquid Crystals; Liquid-Crystal Devices. RESUMEN:En este trabajo se propone un nuevo algoritmo para resolver la posición molecular del cristal liquido nemático (CLN) en un dispositivo afectado por un campo eléctrico. La formulación característica del CLN bajo la influencia de un campo eléctrico se compone de la energía libre de deformación de Frank-Oseen menos la energía eléctrica. Este resultado, considerado como energía libre de Gibbs, tiene un mínimo cuando el director molecular se encuentra en equilibrio. La minimización de esta energía ha sido establecida usando una representación esférica del director molecular. Se han considerado las constantes elásticas del CLN y se ha resuelto mediante métodos numéricos. Para ello se emplea un algoritmo desarrollado por los autores, que ha sido comparado con otros métodos propuestos en la literatura como el método de las diferencias finitas (FDT) o un método de resolución propietario de MATLAB conocido como bvp4c. Las comparativas realizadas muestran un comportamiento superior del algoritmo propuesto, siendo más rápido y preciso que los métodos anteriores. Una vez que se conoce la posición de las moléculas en el dispositivo, otros parámetros como índice de refracción y permitividad en función del voltaje, pueden ser determinados. Para dar una validez a los resultados de simulación, se ha fabricado y caracterizado un dispositivo monopixel de CLN. Las medidas experimentales de birrefringencia y permitividad para diferentes tensiones de alimentación muestran una gran concordancia con los resultados de simulación. Este trabajo pretende proporcionar una herramienta de simulación que puede emplearse en otros dispositivos de CLN más complejos en los cuales se conoce l...

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Section: Solving Continuum Theorymentioning

confidence: 99%

“…However, in order to obtain accurate results, numerical methods are required. Recent numerical simulations have focused on NLC in tumbling flows [2], nematic dynamics [3], and new algorithms [4]. The objective of these works is to find the position of the NLC director inside the cell.…”

Section: Introductionmentioning

confidence: 99%

Modeling electro-optical response of nematic liquid crystals by numerical methods

Algorri¹

2013

Opt. Pura Apl.

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“…Cruz et al [32] adaptaram o método GENSMAC3D para calcular escoamentos tridimensionais confinados de cristais líquidos nemáticos sob efeito de forte campo magnético, entre outras novas aplicações do método. Recentemente, Cruz et al [33] fizeram uma adaptação no método GENSMAC e desenvolveram um método de diferenças finitas para resolver escoamentos de cristais líquidos nemáticos em duas dimensões.…”

Section: Uma Revisão Sobre O Método Gensmacunclassified

Solução numérica de escoamentos de cristais líquidos nemáticos

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Numerical investigation of director orientation and flow of nematic liquid crystals in a planar 1:4 expansion

Cited by 2 publications

References 24 publications

Modeling electro-optical response of nematic liquid crystals by numerical methods

Modeling electro-optical response of nematic liquid crystals by numerical methods

Solução numérica de escoamentos de cristais líquidos nemáticos

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