Finite-element modeling of liquid-crystal hydrodynamics with a variable degree of order

James, Richard; Willman, Eero; FernandezFernandez, F.A.; Day, SE

doi:10.1109/ted.2006.876039

Cited by 84 publications

(81 citation statements)

References 25 publications

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“…Equilibrium configurations of the liquid crystal are found by minimizing the Landau-de Gennes free-energy functional using the finite-element method over a mesh of tetrahedra [32,33]. The liquid crystal is described by an order tensor (Q-tensor) representation that takes into account the head-tail symmetry of the nematic director and allows for order parameter variations and biaxiality.…”

Section: Numerical Modelmentioning

confidence: 99%

“…More pronounced patterned surfaces induce large distortions in the director field, leading to defects. In this case, one must resort to the Landau-de Gennes Q-tensor theory in conjunction with numerical methods if defects are to be treated accurately [32][33][34]. In cases with sufficiently small patterns, molecular simulations have also been used to examine the anchoring effect and LC orientation near the patterns [11,35].…”

Section: Introductionmentioning

confidence: 99%

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Liquid crystal alignment induced by micron-scale patterned surfaces

et al. 2014

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Induced bulk orientation of nematic liquid crystal in contact with micron-scale patterned surfaces is investigated using the Landau-de Gennes theory by means of three-dimensional simulations. The effect of the size and spacing of square cross-sectional well and post patterns is investigated and shown to influence the orientation of the liquid crystal bulk, far removed from the surface. Additionally, the effective anchoring strength of the induced alignment is estimated using a modified version of the torque balance method. Both azimuthal and zenithal multistability are shown to exist within unique ranges of feature sizes.

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Section: Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Liquid crystal alignment induced by micron-scale patterned surfaces

et al. 2014

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“…The viscous flow properties of the liquid crystal material are described in both hydrodynamic theories by the Miesowicz coefficients. A finite element implementation, 14 in a one-dimensional version, is used to calculate the liquid crystal hydrodynamics of the test cells. Material coefficients for the simulation at 20°C are obtained from the available liquid crystal datasheets.…”

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confidence: 99%

Effect of material properties on reverse flow in nematic liquid crystal devices with homeotropic alignment

Vanbrabant

Beeckman

Neyts

et al. 2009

Applied Physics Letters

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Reverse flow is undesirable in liquid crystal devices with vertical alignment. The influence of the material properties on the onset of backflow is investigated for commercially available negative dielectric liquid crystals. It is shown that the threshold voltage V BF for the occurrence of backflow is an important material characteristic. This threshold is relevant for applications and a large value is desired in devices to avoid backflow while keeping a wide applicable voltage range. Accurate finite element simulation of the liquid crystal hydrodynamics allows extraction of V BF and the unknown Miesowicz coefficients ij . The resulting values are tabulated at 20.0°C. © 2009 American Institute of Physics. ͓doi:10.1063/1.3242018͔The occurrence of reverse nematic flow 1 in liquid crystal devices with homeotropic alignment 2,3 has important consequences for practical applications. For instance, vertically aligned liquid crystal displays ͑VA-LCDs͒ have become very popular for mobile and television applications because of their excellent contrast ratio and wide viewing angle. However, their dynamic behavior 4 is affected by the possible occurrence of reverse flow, also referred to as backflow. When a voltage step with amplitude exceeding a certain threshold V BF is applied, the initial rapid variation causes reverse flow of the negative dielectric liquid crystal which leads to a complex reorientation mechanism ͑including a twist deformation͒ and a bounced transient transmission profile, 5 increasing the switching times. Therefore, the limitations due to backflow must be taken into account as a special case to design improved driving schemes 6 to achieve fast and reliable switching in VA-LCDs. In this paper, the influence of the material properties on the onset of backflow is investigated for a number of commercially available liquid crystal materials with negative dielectric anisotropy. The viscous flow properties of liquid crystals are described by the four Miesowicz 7 coefficients ij . The three principal coefficients express the viscosity of the liquid crystal for a liquid crystal director parallel to the direction of flow ͑ 11 ͒, parallel to the direction of the velocity gradient ͑ 22 ͒, and perpendicular to both previous directions ͑ 33 ͒, respectively. The fourth coefficient 12 is related to the shear viscosity. The ij coefficients are, in general, not known because of the notorious difficulty in measuring their values accurately. 8 It is shown that the threshold voltage V BF for the occurrence of backflow is a material characteristic comparable to the Freedericksz threshold voltage 9 for elastic deformation. The backflow threshold is related to the viscous flow properties of liquid crystals and is relevant for practical devices because backflow is undesired and should be avoided. Furthermore, it is possible to estimate the unknown Miesowicz viscosity coefficients ij based on measurement and simulation of V BF . The ij coefficients are extracted using this approach and tabulated together with the V BF values at...

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“…Consequently, the biaxial Q-tensor has five independent coefficients so that it can be described by the representation (see, for example, SONNET, KILIAN AND HESS [51], JAMES ET AL. [28] and MACDONALD ET AL. [36])…”

Section: Uniaxial and Biaxial Nematicsmentioning

confidence: 95%

“…[28]. In general it can be stated that the nematic mesogens orient themselves with their major axis in the direction of the electric field whenever > ⊥ .…”

Section: Dielectric Energy ψ Dielmentioning

confidence: 99%

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

Keip

Nadgir

2017

GAMM-Mitteilungen

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The present contribution proposes a continuum-mechanical phase-field approach to model the electro-elastic behavior of nematic liquid crystal elastomers. The nemato-electro-elastic model is embedded into the fundamental Landau-de-Gennes theory for isotropic-nematic phase transition and employs a tensorial order parameter as the phase field. Nematic deformations are incorporated through a constitutive ansatz in terms of the order parameter. The phase-field formulation is implemented into the finite element method, so that the microstructure evolution of nematic elastomers under different boundary conditions can be studied. We show that the model is capable to capture characteristic features of nematic elastomers including mechanically and electrically induced microstructure evolution as well as the occurrence of stripe domains.

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Finite-element modeling of liquid-crystal hydrodynamics with a variable degree of order

Cited by 84 publications

References 25 publications

Liquid crystal alignment induced by micron-scale patterned surfaces

Liquid crystal alignment induced by micron-scale patterned surfaces

Effect of material properties on reverse flow in nematic liquid crystal devices with homeotropic alignment

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

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