Numerical analysis of nematic liquid crystal alignment on asymmetric surface grating structures

The influence of an asymmetric periodic grooved cell surface on the 2D static director configuration of a nematic liquid crystal has been investigated. The minimum in the Frank-Oseen free energy was solved numerically with the Rapini-Papoular form of the surface anchoring energy at the nematic-grating interface. Results are presented for the variation of pretilt angle in the tilted bulk director field as a function of the surface groove depth, pitch and asymmetry and the bulk parameters. The simulations demonstrate the existence of two energetically degenerate high and low pretilted bulk alignment configurations. The pretilt values in these two regimes and also for the low tilt regime with finite surface anchoring are consistent with experimental results. An effective increase in the resolution of the model is obtained by using an irregular grid to describe the surface profile.     

Pretilt angle of liquid crystals and liquid-crystal alignment on microgrooved polyimide surfaces fabricated by soft embossing method

In this study, the soft embossing method is proposed to fabricate periodical microgrooved structure on polyimide surfaces. These microgrooved polyimide surfaces are assembled to form liquid-crystal cells. It is found that the director of liquid crystals uniformly aligns along the groove direction even when the groove width is as high as 3 microm. The anchoring energy of these microgrooved polyimide surfaces is higher than that of the typical rubbed surfaces. The pretilt angle of liquid crystals is adjusted by tuning the surface polarity of the polyimide alignment layer, which is identified by the advancing contact angle of water. The surface polarity of polyimide alignment layers is manipulated by simply mixing two kinds of polyimide: a more hydrophilic one and a more hydrophobic one. It is found that the pretilt angle of liquid crystals increases along with the advancing contact angle of water on the alignment layer under the condition of a fixed surface topography.     

Optical response of a nematic liquid crystal cell at the splay – bend transition: a model and dynamic simulation

We study the dynamical optical response of a nematic liquid crystal cell that undergoes the splay–bend transition after applying a voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model are solved numerically to calculate the temporal evolution of the director profile and of the transmittance. We evaluate the response time as a function of a number of parameters, such as dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity.     

Optical response of a nematic liquid crystal cell at the splay - bend transition: a model and dynamic simulation

We study the dynamical optical response of a nematic liquid crystal cell that undergoes the splay-bend transition after applying a voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model are solved numerically to calculate the temporal evolution of the director profile and of the transmittance. We evaluate the response time as a function of a number of parameters, such as dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity.     

Control of surface anchoring properties of liquid crystal by thermo-transfer printing of siloxane oligomers

We presented the results for the surface anchoring properties of a nematic liquid crystal (LC) in a wide range of the substrate wettability through thermo-transfer printing of siloxane oligomers. For the modification of the surface energy, poly(dimethylsiloxane) (PDMS) oligomers were directly transferred onto a glass substrate from a bulk PDMS plate by contact printing at elevated temperatures. The hydrophobicity of the PDMS-modified surface was found to increase with the temperature of the substrate during transfer printing. The LC alignment on the PDMS-modified substrate exhibited continuous variations of the pretilt angle from nearly 0° to 90° and the polar anchoring strength according to the surface energy.     

Determination of coherence length of a smectic liquid crystal

A model for the near surface director profile in a homeotropically aligned smectic liquid crystal is developed based on the idea of the two independent anchoring energies separately associated with the director and the density wave at the surface. These anchoring energies are counterbalanced by the tendency to form the smectic C phase in the bulk. The model yields simple distance-dependent cone angle profiles which are compared with experimental data obtained from the half-leaky waveguide technique to obtain the coherence length for the penetration of the smectic C phase into the smectic A phase and the ratio of the surface to bulk cone angles.     

Liquid crystal alignment capabilities on rubbed organic solvent soluble polyimide surfaces with trifluoromethyl moieties

High pretilt angles, polar anchoring energy (out of plane-tilt), and surface ordering in the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB) were investigated on rubbed organic solvent soluble polyimide (PI) surfaces with a helical backbone structure and trifluoromethyl moieties. It was found that the pretilt angle of 5CB is about 15° in the wide rubbing region of rubbed soluble PI surfaces with trifluoromethyl moieties attached to the lateral benzene rings. It is suggested that the microscopic surface structure of the polymer contributes to the LC pretilt angle generation at the surface. Also, the polar anchoring energy of 5CB is dependent on the molecular structure of these unidirectionally rubbed soluble PI surfaces. The polar anchoring strength of 5CB on rubbed soluble PI surfaces is as weak with trifluoromethyl moieties attached to the lateral benzene rings weak as when the trifluoromethyl moieties are attached to the polymer backbone. Finally, the polar anchoring energy of 5CB strongly depends on the surface ordering of rubbed soluble PI surfaces.     

Effect of pretilt angle on the polar anchoring energy in NLCs on weakly rubbed polyimide surfaces

The polar anchoring strength and pretilt angle generation in nematic liquid crystals (NLCs), on three kinds of rubbed polyimide (PI) surfaces, were investigated. The pretilt angle generated in 4-n-pentyl-4'-cyanobiphenyl (5CB) is large compared with ZLI-4792 (a fluorinated mixture type NLC) for all rubbed PI surfaces. The high pretilt angle in 5CB is attributed to a much larger birefringence and much larger perpendicular component of permittivity. The polar anchoring energy of ZLI-4792 is high compared with 5CB on all rubbed PI surfaces for a weak rubbing strength. It is suggested that the high anchoring energy of ZLI-4792 may be attributed to the low NLC pretilt angle.     

Relationship between alignment layer polymer surface structures and liquid crystal display parameters

The polar alignment layer (AL) surface provided relatively small liquid crystal (LC) pretilt angles while polyimides with long alkyl side chains gave relatively large LC pretilt angles. The results suggest that LC pretilt angles, in addition to an anchoring effect, are greatly affected by both electronic and steric interactions between LC molecules and a polyimide alignment layer surface. Rubbing with a cotton cloth induces functional groups, side chains, and repeat units at the surface of a liquid crystal polyimide AL to re-orient. It was discovered that rubbing induced polar functional groups and repeat units to re-orient out-of-the-plane of the surface, and it made non-polar aliphatic side chains partially re-orient inwards, toward the bulk of the film.     

Liquid crystal alignment capabilities on rubbed organic solvent soluble polyimide surfaces with trifluoromethyl moieties

High pretilt angles, polar anchoring energy (out of plane-tilt), and surface ordering in the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB) were investigated on rubbed organic solvent soluble polyimide (PI) surfaces with a helical backbone structure and trifluoromethyl moieties. It was found that the pretilt angle of 5CB is about 15° in the wide rubbing region of rubbed soluble PI surfaces with trifluoromethyl moieties attached to the lateral benzene rings. It is suggested that the microscopic surface structure of the polymer contributes to the LC pretilt angle generation at the surface. Also, the polar anchoring energy of 5CB is dependent on the molecular structure of these unidirectionally rubbed soluble PI surfaces. The polar anchoring strength of 5CB on rubbed soluble PI surfaces is as weak with trifluoromethyl moieties attached to the lateral benzene rings weak as when the trifluoromethyl moieties are attached to the polymer backbone. Finally, the polar anchoring energy of 5CB strongly depends on the surface ordering of rubbed soluble PI surfaces.     

Generalised technique for calculation of plane director profiles in bounded nematic liquid crystals

We propose an improved conformal mapping technique for analytical calculation of two-dimensional profiles of the nematic liquid crystal (NLC) director in a cell with a simply connected cross-sectional region. We consider the case of the strong anchoring and the piecewise constant director pretilt on the piecewise smooth curve which bounds the region. Obtained expressions for the director profile explicitly depend on the conformal mapping which maps the region onto the upper half plane of a complex plane. An advantage of our method in comparison with the standard conformal mapping technique is that it does not require the knowledge of the inverse mapping and the calculation of the integral in the Poisson formula. Proposed technique allows to take into account topological defects in the bulk of the NLC on the symmetry axis of the region. As an example of how the method can be used, we find an analytical expression for the director profile in a horizontal cylindrical groove partly filled with the NLC. We consider the case where a disclination line parallel to the axis of the groove occurs in the bulk of the NLC. The equilibrium position of the disclination line is found.     

A thermodynamic approach to the anchoring phenomenon in the nematic liquid crystal-substrate system

The phenomenon of anchoring in the nematic liquid crystal-amorphous substrate system is considered and model independent definitions of the surface nematic director, the surface tension and the anchoring energy coefficient are proposed. Then the Landau-de Gennes model of the system is studied for a specific choice of the surface parameters, which leads to a continuous homeotropic-conical anchoring transition. The free energy as a function of the director at a distance l from the surface is found. It is shown that its form is different in two regions of the temperature-distance plane separated by the line of a Freedericksz transition. The asymptotic behaviour of the free energy for large l and for infinitesimal deviations of the director from the anchoring direction is studied. It is found that the asymptotic formula holds also in the vicinity of the anchoring transition. Finally, the results of numerical studies of the Landau-de Gennes model are compared with the predictions of a simple phenomenological model.     

Dynamic behaviour at a nematic liquid crystal-rubbednylon interface using evanescent wave photon correlation spectroscopy

Photon correlation spectroscopy of light scattered by director fluctuations from an evanescent optical wave propagating in the nematic liquid crystal 5CB is used to study the interfacial dynamic behaviour of the liquid crystal. The intensity correlation function of light scattered by interfacial orientation fluctuations is measured by illuminating to give a short optical penetration depth within the nematic. These surface scattering correlation functions strongly differ from the bulk correlation function and are interpreted in terms of a nematic surface orientation mode arising from the coupling between the director field and the fluid velocity. It is shown that the analysis of the surface mode gives a method for measuring anchoring energies in liquid crystals. The anchoring energy obtained for rotation of the director away from the rubbing direction about an axis normal to the surface for 5CB at a rubbed nylon surface is 7.14±0.7 × 10-² ergcm-².     

Influence of anchoring at a nematic cell surface on threshold spatially periodic reorientation of a director

We have analysed the influence of surface director anchoring in a planar flexoelectric nematic cell on the threshold spatially periodic reorientation of the director in an external dc electric field. By minimizing the free energy of the nematic cell we obtained the equations for a director and numerically solved them in the one elastic constant approximation. The dependences of the threshold electric field and the spatial period of director structure on the azimuthal and polar anchoring energy, as well as the flexoelectric parameters, are determined. It is shown that the domain of the flexoelectric parameter values, at which the spatially periodic reorientation of a director takes place, increases with decreasing azimuthal anchoring energy and increasing polar anchoring energy.     

Liquid crystal orientation by holographic phase gratings recorded on photosensitive Langmuir-Blodgett films

Holographic gratings were recorded on photosensitive Langmuir-Blodgett films characterized by UV spectroscopy, birefringence measurements and atomic force microscopy. Different polarizations of Ar laser writing beams create particular patterns of chromophore orientation in the diffraction spots. The gratings were shown to orient a nematic liquid crystal with the director parallel to the axes of the chromophores predetermined by film irradiation. In the case of the sp grating (recorded with laser beams polarized perpendicular to each other), two equivalent easy directions for the liquid crystal orientations at 90degree with respect to each other were observed; that is a quasi-bistable anchoring interface had been prepared. Measurements of the pretilt angles theta1s and anchoring energy Ws of 5CB on different holographic gratings show that this orientation technique is very promising for display technology.     

Surface viscosity and reorientation process in an asymmetric nematic cell

The influence of surface viscosity and anchoring energy on the reorientation process of a nematic liquid crystal cell is theoretically investigated. The cell is a slab of thickness, d, whose limiting surfaces are characterised by different anchoring strengths and present easy directions parallel to the bounding surfaces, changing with time due to some external action. The exact space-time profile of the director angle is obtained by means of integral transform techniques and a Green function approach. From this formalism, the time dependence of the optical path difference is exactly determined and its behaviour is analysed in connection with the presence of surface viscosity and different anchoring energies. The problem is also exactly solved in the presence of a constant electric field. It is shown that the compatibility problem between the time derivative of the director field on the surface and in the bulk can be avoided.     

Analytical determination of anchoring energy coefficient in liquid crystal cells

An analytical solution for the anchoring energy coefficient of liquid crystal (LC) cells with arbitrary values of pretilt angles is derived. When phase retardation is plotted against applied voltage, one acquires the extrapolation length of the anchoring, and the anchoring energy coefficient is derived in the low-voltage regime. This solution can be applied to LC cells with various pretilt angles straightforwardly. Finally, the anchoring energy coefficient of 4.9 × 10^?5 J/m² is obtained for a homemade LC cell with a pretilt angle of 32.7°.     

Second order elasticity in nematics: A new anchoring source

By considering, in the expression of the nematic free energy density, an additional term in the square of the director second derivatives, an unexpected anchoring source results, due only to surface and bulk elastic constants. As an example, the case of a planar homogeneous and of a homeotropic nematic cell, equally anchored on both walls, is discussed. In both situations the new anchoring source has a destabilizing effect.     

Effects of pretilt angle and anchoring energy on alignment of uniformly lying helix mode

We investigated the effects of pretilt angle and anchoring energy on the formation of a uniformly lying helix (ULH) texture of cholesteric liquid crystals (CLCs). Pretilt angle was controlled by the thickness of a vertical alignment layer coated onto a planar alignment layer. In the given pretilt angle, the anchoring energy was enhanced by introducing reactive mesogen to the vertical alignment material. To characterise quantitatively the formation of the ULH texture we introduced reflectance, governed by areas of the ULH region and the planar-aligned CLC region. We found that the ULH texture was more widely formed under the condition of higher pretilt angle and weaker anchoring energy. Also, a more uniform alignment of the ULH texture was achieved with the higher pretilt angle even under the same anchoring energy condition.     

Modelling of director equilibrium states in a nematic cell with relief surface

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail.