Nigel J. Mottram

Multistable alignment states in nematic liquid crystal filled wells

Two distinct, stable alignment states have been observed for a nematic liquid crystal confined in a layer with thickness of 12μm and in square wells with sides of length between 20 and 80μm. The director lies in the plane of the layer and line defects occur in two corners of the squares. The positions of the defects determine whether the director orientation is across the diagonal or is parallel to two opposite edges of the square. The device is multistable because both the diagonal and parallel states are stable when rotated by multiples of 90° in plane.

Electric fields can control the transport of water in carbon nanotubes

The properties of water confined inside nanotubes are of considerable scientific and technological interest. We use molecular dynamics to investigate the structure and average orientation of water flowing within a carbon nanotube. We find that water exhibits biaxial paranematic liquid crystal ordering both within the nanotube and close to its ends. This preferred molecular ordering is enhanced when an axial electric field is applied, affecting the water flow rate through the nanotube. A spatially patterned electric field can minimize nanotube entrance effects and significantly increase the flow rate.

Defect-induced melting in nematic liquid crystals

In this paper we employ a relatively simple theory to show how a nematic disclination line can act as a nucleation site for the growth of the isotropic phase. With this theory we are able to find analytical expressions for the critical temperature of nucleation and the behaviour of the core radius as a function of temperature. We are then able to compare these results with a previous numerical model of this effect.

Conformal mapping techniques for the modelling of liquid crystal devices

In this paper, we review a number of uses of conformal mapping techniques for obtaining director profiles of liquid crystals in confined and semi-confined geometries. In particular, we will consider geometries which allow more than one stable state, some of which are of use in bistable displays. These solutions also allow the investigation of the energy of stable states and enable conclusions to be reached as to how such geometries may be optimised for bistable display applications. Such techniques are also able to provide initial configurations for the solution of more complicated situations where numerical methods are used to investigate switching characteristics.

Deformation of a nearly-hemispherical conducting drop due to an electric field: theory and experiment

We consider, both theoretically and experimentally, the deformation due to an electric field of a pinned nearly hemispherical static sessile drop of an ionic fluid with a high conductivity resting on the lower substrate of a parallel-plate capacitor. Using both numerical and asymptotic approaches, we find solutions to the coupled electrostatic and augmented Young–Laplace equations which agree very well with the experimental results. Our asymptotic solution for the drop interface extends previous work in two ways, namely, to drops that have zero-field contact angles that are not exactly π/2 and to higher order in the applied electric field, and provides useful predictive equations for the changes in the height, contact angle, and pressure as functions of the zero-field contact angle, drop radius, surface tension, and applied electric field. The asymptotic solution requires some numerical computations, and so a surprisingly accurate approximate analytical asymptotic solution is also obtained.

Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces

A layer of insulating liquid of dielectric constant ɛOil and average thickness h− coats a flat surface at y = 0 at which a one-dimensional sinusoidal potential V(x,0)=VOcos(πx/p) is applied. Dielectrophoresis forces create a static undulation (or “wrinkle”) distortion h(x) of period p at the liquid/air interface. Analytical expressions have been derived for the electrostatic energy and the interfacial energy associated with the surface undulation when h(x)=h−-(1/2)Acos(2πx/p) yielding a scaling relationship for A as a function of h−, p, VO, ɛOil and the surface tension. The analysis is valid as A/p → 0, and in this limit convergence with numerical simulation of the system is shown.

Sidewall control of static azimuthal bistable nematic alignment states

Stable azimuthal alignment states have been created in the plane of a homogeneous layer of nematic liquid crystal by the action of one or more sawtooth sidewalls. The alignment states in devices with two sawtooth sidewall structures, either in-phase or in antiphase, and with one sawtooth wall opposite a flat wall have been investigated as a function of the sawtooth pitch. The optical textures of the observed states are in excellent agreement with the predictions of nematic Q-tensor theory. The frequencies of occurrence of the different states are broadly consistent with the expected inverse correlation with the Q-tensor predictions for their energy.

A mathematical model for blade coating of a nematic liquid crystal

The standard industrial process of blade‐coating is now being used to produce new liquid crystal displays (LCDs) in which a liquid crystal and optical layers are coated onto a substrate. Motivated by this new LCD manufacturing process, we use the Ericksen–Leslie equations to develop a simple mathematical model for blade coating of a nematic liquid crystal. The direction and uniformity of the director are important factors for the performance of the displays, particularly when this alignment is ‘frozen in’ within optical layers. For this reason we investigate the flow and director within a liquid crystal film both after emerging from the region under a blade (the so‐called ‘drag‐out’ problem) and before entering the region under a blade (the so‐called ‘drag‐in’ problem). We restrict our attention to thin films and small director angles, and we study two particular cases in which either orientational elasticity effects or flow effects dominate the alignment of the liquid crystal. We find that there is a unique solution of the drag‐out problem, whereas there may be multiple solutions of the drag‐in problem. When orientational elasticity effects dominate we obtain a simple analytical solution for the director. When flow effects dominate we find that the director is uniform in the bulk of the liquid crystal, which exhibits thin orientational boundary layers near the substrate and the free surface, within which the director orientation changes rapidly from its prescribed boundary value to the flow alignment angle. These boundary layers may be potential locations for the nucleation of defects.

Shear-driven and pressure-driven flow of a nematic liquid crystal in a slowly varying channel

Motivated by the industrially important processes of blade coating and cavity filling of liquid crystalline materials, we consider steady, two-dimensional shear-driven (Couette) and pressure-driven (plane Poiseuille) flow of a thin film of a nematic liquid crystal in the slowly varying channel formed between a fixed blade of prescribed shape and a planar substrate. Specifically, blade coating motivates the study of shear-driven flow due to the motion of the substrate parallel to itself with constant velocity, while cavity filling motivates the study of pressure-driven flow due to an imposed pressure drop. We use a combination of analytical and numerical techniques to analyze the Ericksen-Leslie equations governing the fluid velocity and pressure and the director orientation in cases when both the aspect ratio of the channel and the distortion of the director field are small. We demonstrate a variety of flow and director-orientation patterns occurring in different parameter regimes. In the limit of weak fl...

Static alignment states in a bistable azimuthal nematic device with blazed grating sidewalls

Bistable azimuthal alignment has been produced in channels of homogeneous nematic liquid crystal with periodic grating sidewalls. The grating morphologies included a symmetric triangular profile (blaze/pitch (b/p) = 0), an asymmetric highly blazed sawtooth profile (b/p = 0.5) and profiles with different amounts of blaze asymmetry between these two extremes. The observed optical textures and the trend in the relative frequency of occurrence of the two stable states as a function of the asymmetry were in agreement with the predictions of n-director-based Frank–Oseen nematic continuum theory. A sidewall grating morphology with an intermediate degree of blaze asymmetry, b/p = 0.3, gave the highest optical contrast between the bistable states.