Liquid crystal VAN tilt bias by surface relief patterning

Liquid Crystal Displays require controlled alignment of the liquid crystal molecular director at its confining surfaces. These surfaces may be coated glass or in the case of 'Liquid Crystal On Silicon' (LCOS) technology, a silicon backplane. In the case of Vertically Aligned Nematic (VAN) cells an initially vertical orientation is used and from this the director may tilt in any direction. Some means is required to bias the tilt in a consistent direction to avoid the occurrence of differently oriented domains. For VAN cells one tilt bias method is oblique deposition of silicon oxide. An alternative method which eliminates concerns over consistency of deposition angle over a large substrate area is the use of surface relief structures to induce tilt bias. This is attractive for LCOS devices. Liquid crystal modelling tools [1] have been used to simulate the effects of rectangular and triangular shaped 'bumps' and 'dips' protruding from and extending into the LC's enclosing surfaces respectively. The director orientation and optical transmission of the LC pixels biased in this way are examined as a function of time during the switching cycle and spatially across the pixel to show that the combination provides controllable tilt bias

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

A finite-element model of liquid-crystal hydrodynamics based on the Qian and Sheng formulation has been developed. This formulation is a generalization of the Ericksen-Leslie theory to include variations in the order parameter, allowing for a proper description of disclinations. The present implementation is well suited to treat properly the various length scales necessary to model large regions yet resolve the rapid variations in the order parameter in proximity to disclinations

Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory

The anisotropic anchoring effect of a treated solid surface on a nematic liquid crystal is described in the Landau-de Gennes theory using a power expansion on the tensor-order parameter and two mutually orthogonal unit vectors. The expression has three degrees of freedom, allowing for independent assignment of polar and azimuthal anchoring strengths and a preferred value of the surface-order parameter. It is shown that in the limit for a uniaxial constant-order parameter, the expression simplifies to the anisotropic generalization of the Rapini-Papoular anchoring energy density proposed by Zhao et al. Experimentally measurable values with a physical meaning in the Oseen-Frank theory can be scaled and assigned to the scalar coefficients of the tensor-order-parameter expansion. Results of numerical experiments comparing the anchoring according to the study of Zhao et al. in the Oseen-Frank theory and the power expansion in the Landau-de Gennes theory are presented and shown to agree well

Liquid crystal droplets under extreme confinement probed by a multiscale simulation approach

In this work, we computationally investigate liquid crystal (LC) droplets in the size range 0.03–1 μm, confined within shells of combined anchoring conditions. Two different types of surface were defined to promote homeotropic and planar degenerate anchoring, respectively. We identified the LC behaviour within the nanoscale droplets using a bespoke multiscale simulation approach. To study 30 nm droplets, we used coarse grained simulations within the dissipative particle dynamics formalism; to study 0.1 μm and larger droplets, we used a finite element method based on the Landau–de Gennes theory. Good agreement between the two methods was observed in our prior analysis and was confirmed in the present work. We explicitly study droplets of size 0.1 and 1 μm by using continuum mechanics calculations. Our results for the largest droplet are consistent with those available in the literature, suggesting that the extension to smaller droplets presented here is realistic, and therefore can be helpful for innovations in which device intensification could be achieved using LC nanodroplets

Engineered liquid crystal nano droplets: insights from multi-scale simulations

Liquid crystal (LC) droplets have been investigated for a wide range of applications, from displays to sensors. Over the years, a need has arisen for complete understanding of the behaviour of LCs in droplets under different conditions for the development of advanced devices, for which accurate modelling is necessary. We show here, for the first time, both qualitative and quantitative agreement between coarse-grained molecular models and Q-tensor theory calculations for liquid crystal (LC) droplets. The approach is demonstrated for two types of droplet surfaces, which possess strong planar degenerate and strong homeotropic anchoring, respectively. Once its reliability has been proven, our approach was used to identify defects due to changes in anchoring in a small region on the LC droplet surface, which could be triggered, for example, by the adsorption of a nano-particle or a protein. Both coarse-grained simulations and Q-tensor analysis show the appearance of defects in well-determined locations within the LC droplet, albeit sometimes affected by degeneracy due to the symmetry of the systems being investigated. These results suggest the possibility of using LC droplets, in the future, as platforms for advanced sensing as well as for signal intensification

3D Modelling of Twist Wall at the Electrode Edge of Liquid Crystal Cells

Q-tensor simulation of the liquid crystal structure at the edge of electrodes has been carried out. The modeling shows a twist wall, which reverses direction to form a zig-zag structure. The results are compared with experiment. Also a defect loop is found in micro-lenses formed using a hole electrode structure