Alan James Leadbetter,D.Sc., FRSC,CBE, 28th March 1934 – 11th March 2019

In cholesteric liquid crystals with a positive dielectric anisotropy, the relaxation from the electric field-aligned director configuration to the stable zero field director configuration proceeds via a metastable transient planar director configuration which has a pitch distinct from the equilibrium state. The transition from the transient planar to the equilibrium zerofield state is shown here to occur via a Helfrich-type instability which continuously leads to an in-plane helical structure. The equilibrium planar state is then seen to grow continuously from the in-plane state, leaving behind walls whose length then spontaneously shrinks.     

Novel structures of a smectic C* phase with high spontaneous polarization in free-standing films

New stable structures of the liquid crystalline smectic C* phase are observed in free standing films of a material with high spontaneous polarization. A stable configuration of thick films is a stripe of state with an in-plane rotation of the director. In ultra-thin films an anisotropic state was observed. The director fields of the observed structures are modelled and compared with theoretical predictions.     

Computer simulation of the homeotropic to planar transition in cholesteric liquid crystals

The transition from the homeotropic to the planar state in cholesteric liquid crystal displays is investigated through computer simulation. The simulation reproduces the observed relaxation from the homeotropic state to the long pitch transient planar state. The simulation also agrees with the suggestion that the transition from the transient planar state to the planar state proceeds through a bulk modulation resulting in folding and buckling of cholesteric layers without introduction of defect cores. The model obtained agrees well with earlier experimental observations showing that the process includes a tilting of cholesteric helices, and that the surface plays only a minor role in the relaxation process.     

Computer simulation of the homeotropic to planar transition in cholesteric liquid crystals

The transition from the homeotropic to the planar state in cholesteric liquid crystal displays is investigated through computer simulation. The simulation reproduces the observed relaxation from the homeotropic state to the long pitch transient planar state. The simulation also agrees with the suggestion that the transition from the transient planar state to the planar state proceeds through a bulk modulation resulting in folding and buckling of cholesteric layers without introduction of defect cores. The model obtained agrees well with earlier experimental observations showing that the process includes a tilting of cholesteric helices, and that the surface plays only a minor role in the relaxation process.     

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.     

Relationship between the pitch and elastic constants of the transient planar state in cholesteric liquid crystals

We investigate experimentally the relationship between the pitch and the elastic constants of a transient planar state in cholesteric liquid crystals. The pitch of the transient planar state is measured by the optical reflection technique. The twist and bend elastic constants of cholesteric materials are determined from the measured values of the threshold voltages for the transitions between a focal-conic state and a homeotropic state. By comparing these values, we experimentally confirm the relationship for the pitch of a transient planar state; P_transient=(K₃₃/K₂₂)P₀, which has been suggested theoretically.     

Orientational transition in the cholesteric layer induced by electrically controlled ionic modification of the surface anchoring

A reorientation of cholesteric liquid crystal with a large helix pitch induced by the electrically controlled ionic modification of the surface anchoring has been studied. In initial state, the cholesteric helix is untwisted completely owing to the normal surface anchoring specified by the cations adsorbed at the substrates. As a result, the homeotropic director configuration is observed within the cell. Under the action of DC electric field, one of the substrates becomes free from the layer of surface active cations, therefore, setting the planar surface anchoring. The latter, in turn, leads to the formation of the hybrid chiral structure. The threshold value and dynamic parameters have been estimated for this process as well as the range of control voltages, which do not allow the electrohydrodynamic instabilities. The twisted hybrid director configuration observed in the experiment has been analysed by means of the simulation of polarisation change of light propagating through the cholesteric layer with asymmetric (planar and homeotropic) surface anchoring on the cell substrates.     

Photo-reversible liquid crystal alignment using azobenzene-based self-assembled monolayers: comparison of the bare monolayer and liquid crystal reorientation dynamics

Photosensitive surfaces treated to have in-plane structural anisotropy by illumination with polarized light can be used to orient liquid crystals (LCs). Here we report a detailed study of the dynamic behavior of this process at both short and long times, comparing the ordering induced in the bare active surface with that of the LC in contact with the surface using a high-sensitivity polarimeter that enables detailed characterization of the anisotropy of the active surface. The experiments were carried out using self-assembled monolayers (SAMs) made from dimethylaminoazobenzene covalently bonded to a glass surface through a triethoxysilane terminus. This surface gives planar alignment of the liquid crystal director with an azimuthal orientation that can be controlled by the polarization of actinic light. We find a remarkable long-term collective interaction between the orientationally ordered SAM and the director field of the LC: while an azobenzene based SAM in contact with an isotropic gas or liquid relaxes to an azimuthally isotropic state in the absence of light due to thermal fluctuations, an orientationally written SAM in contact with LC in the absence of light can maintain the LC director twist permanently, that is, the SAM is capable of providing azimuthal anchoring to the LC even in the presence of a torque about the surface normal. We find that the short-time, transient LC reorientation is limited by the weak azimuthal anchoring strength of the SAM and by the LC viscosity.     

Electrically controlled director slippage over a photosensitive aligning surface; in-plane sliding mode

We have studied the electro-optical characteristics of a homogeneously aligned nematic liquid crystal (LC) with weak planar anchoring of the director at the bounding substrates. By using the in-plane switching (IPS) of the LC which is achieved by an in-plane electric field, the driving voltage was confirmed to be far less than that of the conventional IPS mode in which both substrates possess strong anchoring characteristics. Moreover, because of the absence of strong subsurface director deformations, the cell could operate optically in the Mauguin regime. Using these features we propose a new type of LC switching mode - in-plane sliding (IPSL) mode. We have realized this mode in a LC cell comprising one reference substrate with strong director anchoring and one substrate covered with photoaligning material with weak anchoring. In order to clarify the switching process, we derived a simplified expression for the threshold voltage on the assumption of uniformity of the in-plane electric field. For the dynamical response of the LC to the in-plane electric field, the switching on and off relaxation times of the IPSL mode were found to be longer than for the traditional IPS mode. However, we have proposed an optimized cell geometry for the IPSL mode with a response time comparable to that of the IPS mode.     

Efficient energy based modeling and experimental validation of liquid filling in planar micro-fluidic components and networks

This paper presents a model that describes how liquid flow fills micro-fluidic components and networks. As an alternative to computational fluid dynamic (CFD) simulations, we use a constrained energy minimization approach. This approach is based on two assumptions that hold in many micro-fluidic devices: (i) The length scales are small, and we consider slow filling rates, hence fluid momentum and viscous terms are small compared to surface tension forces, consequently the liquid/gas interfaces can be viewed as a succession of quasi-steady equilibrium configurations. (ii) Any equilibrium configuration corresponds to a surface tension energy minima which is constrained by the device shape and the volume of liquid in the device. The model is developed for planar micro-fluidic devices, is based on a fundamental physical principle, and shows accurate agreement with experimental data. It takes us only a few minutes to evaluate the model for a planar component of any shape using the Surface Evolver software, and this is significantly less then the computer run time required for CFD simulations. Moreover, once a library of component models has been created (which takes less than an hour of computer time) it then takes only seconds to simulate different network architectures with thousands of components. This fast "reconfigure the network and simulate in seconds" capability is essential for the design of truly complex networks that will enable the next generation of passive, micro-fluidic, lab-on-a-chip systems.     

Analysis of transient periodic textures in nematic polymers

A numerical solution of the Leslie-Ericksen equations for nematic liquid crystals is obtained for in-plane rotation of a strong magnetic field. A transient periodic orientation develops as a result of in-plane director motion and the induced shear flow. At long times the in-plane director orientation results in steady splay-bend inversion walls. A linear stability analysis shows that the inversion walls are unstable to perturbations out of the plane for elastic coefficients characteristic of nematic polymers. Calculations of transmitted light intensity through crossed polarizers for the computed orientation development predict the evolution of a banded texture, as observed experimentally.     

Liquid crystal alignment on isotropic submicro‐textured surfaces of homeotropic‐planar states

The equilibrium configuration of liquid crystal molecules in contact with a periodicly patterned substrate has been theoretically analysed considering the variation of the order parameter at the interface, and a first order transition was predicted for a critical periodicity, or induced by temperature or an electric field. In this work, we experimentally investigated the equilibrium configuration of the director for a submicron patterned substrate, alternating homeotropic and random planar regions in the substrate. Experimentally, it was possible to access a starting point, theoretically close to the first order transition, however no transition was observed either on varying the temperature or on applying an electric field. The possible reasons for the non‐observation of the phase transition are discussed.     

Liquid crystal alignment on isotropic submicro-textured surfaces of homeotropic-planar states

The equilibrium configuration of liquid crystal molecules in contact with a periodicly patterned substrate has been theoretically analysed considering the variation of the order parameter at the interface, and a first order transition was predicted for a critical periodicity, or induced by temperature or an electric field. In this work, we experimentally investigated the equilibrium configuration of the director for a submicron patterned substrate, alternating homeotropic and random planar regions in the substrate. Experimentally, it was possible to access a starting point, theoretically close to the first order transition, however no transition was observed either on varying the temperature or on applying an electric field. The possible reasons for the non-observation of the phase transition are discussed.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

Abstract

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

Shear flow induced deformations of planar cholesteric layers

The shear flow induced deformation of the planar cholesteric structure is modelled numerically, taking into account long pitch flow-aligning material. Three pitch-to-thickness ratios in five configurations are considered. Unwinding of the cholesteric helix due to the flow alignment is found. This process has a threshold character, when the mid-plane director is perpendicular to the plane of shear; otherwise it is continuous. The transverse component of the flow is always present. At high stress, the director in the prevailing part of the layer is oriented at the flow-aligning angle.     

Periodic deformations induced by a magnetic field in planar twisted nematic layers

Magnetic field-induced spatially periodic deformations of planar nematic layers twisted by an angle Φ were investigated numerically. Chiral nematics with pitches compatible with the twist angle and non-chiral nematics twisted by Φ ≤π/2 were considered. Two different modes of deformation, taking the form of stripes, were found: the so called Mode X, with periodicity parallel to the mid-plane director in the undisturbed structure, and Mode Y with periodicity perpendicular to the mid-plane director. The static director distributions were calculated for various magnetic field strengths, twist angles and elastic parameters. The influence of surface tilt was also investigated. Mode X appeared for sufficiently large Φ and was possible in nematics with typical elastic properties. Mode Y appeared provided that the k₂₂/k₁₁ elastic constant ratio and the twist angle Φ were sufficiently small. Both modes arose from the undistorted state when the magnetic field exceeded a threshold value. The spatial period of the patterns increased with field strength. At high field, regions with almost homogeneous deformation arose in the two halves of each stripe. Their width and, simultaneously, the spatial period diverged to infinity at some critical field. This divergence corresponds to the transition to a homogeneously deformed state. Diagrams were constructed showing the ranges of parameters favouring the periodic distortions.     

Periodic deformations induced by a magnetic field in planar twisted nematic layers

Magnetic field-induced spatially periodic deformations of planar nematic layers twisted by an angle Φ were investigated numerically. Chiral nematics with pitches compatible with the twist angle and non-chiral nematics twisted by Φ ? π/2 were considered. Two different modes of deformation, taking the form of stripes, were found: the so called Mode X, with periodicity parallel to the mid-plane director in the undisturbed structure, and Mode Y with periodicity perpendicular to the mid-plane director. The static director distributions were calculated for various magnetic field strengths, twist angles and elastic parameters. The influence of surface tilt was also investigated. Mode X appeared for sufficiently large Φ and was possible in nematics with typical elastic properties. Mode Y appeared provided that the k ₂₂/k ₁₁ elastic constant ratio and the twist angle Φ were sufficiently small. Both modes arose from the undistorted state when the magnetic field exceeded a threshold value. The spatial period of the patterns increased with field strength. At high field, regions with almost homogeneous deformation arose in the two halves of each stripe. Their width and, simultaneously, the spatial period diverged to infinity at some critical field. This divergence corresponds to the transition to a homogeneously deformed state. Diagrams were constructed showing the ranges of parameters favouring the periodic distortions.     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.