Electrically controlled topological micro cargo transportation.

We demonstrate electrically controlled linear translation and precision positioning of a colloidal particle in a soft matter device. The basis of transportation is the time dependent electric field reconfiguration and manipulation of a topological line defect between two distinct hybrid aligned nematic liquid crystal domains having opposing tilt orientations. Deliberately tuning an applied voltage relative to a low threshold value (5.7 V at 1 kHz) permits defect trapping of the colloidal particle and allows subsequent control over the particle's velocity and bidirectional linear movement over millimeter distances, without the need for externally imposed flow nor for lateral confining walls.

Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring.

Motivated by the one-drop-filling (ODF) method for the industrial manufacturing of liquid crystal displays, we analyze the pressure-driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasisteady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number, the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number, the solution for the director angle is dominated by splay elastic effects with viscous effects appearing at first order. As the Ericksen number varies, there is a continuous transition between these asymptotic behaviors, and in fact the two asymptotic solutions capture the behavior rather well for all values of the Ericksen number. The steady-state value of the director angle at the boundaries and the timescale of the evolution toward this steady-state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method, it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.

Nematic liquid crystal director structures in rectangular regions.

We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyze nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behavior of the director structure and energy for very strong anchoring. We show that in both cases-for the transitions from uniform to distorted states and the limit of infinitely strong anchoring-the approximate analytic expansions agree very well with corresponding numerical calculations of the full model.

Dynamic response of a thin sessile drop of conductive liquid to an abruptly applied or removed electric field.

We consider, both theoretically and experimentally, a thin sessile drop of conductive liquid that rests on the lower plate of a parallel-plate capacitor. We derive analytical expressions for both the initial deformation and the relaxation dynamics of the drop as the electric field is either abruptly applied or abruptly removed, as functions of the geometrical, electrical, and material parameters, and investigate the ranges of validity of these expressions by comparison with full numerical simulations. These expressions provide a reasonable description of the experimentally measured dynamic response of a drop of conductive ionic liquid 1-butyl-3-methyl imidazolium tetrafluoroborate.

Flow-induced delayed Freedericksz transition.

We demonstrate that a compact manometer experiment allows direct observation of a delay to the classical electric-field-induced Freedericksz transition produced by flow in a highly dispersive nematic liquid crystal layer. The Ericksen-Leslie equations are used to show that a flow aligning torque generated in the nematic layer under Poiseuille flow competes with the orthogonal electric-field reorientation torque. This model fully reproduces the experimental results using only self-consistently determined viscosity values, and predicts a more generally applicable expression for the dependence of the delay E(c)∝sqrt[ζ/Δχ(e)] on the shear rate ζ and on the electric susceptibility anisotropy Δχ(e).

Defect trajectories and domain-wall loop dynamics during two-frequency switching in a bistable azimuthal nematic device.

Bistable azimuthal nematic alignment textures have been created in micrometer-scale channels for which one sidewall is smooth and straight and the other possesses a symmetric sawtooth morphology. The optical textures have been observed during dynamic switching between the two stable states in response to dual frequency ac waveform driving of a highly dispersive nematic liquid crystal. The switching processes involves collapsing of filamentlike director reorientation (tilt-wall) loops and the associated motion and annihilation of surface defects along and close to the edge at the sawtooth sidewall. The predictions from both the n-director-based Ericksen-Leslie theory and the Q-tensor theory are in good agreement with the experimental observations.

Flexoelectric instability and a spontaneous chiral-symmetry breaking in a nematic liquid crystal cell with asymmetric boundary conditions.

Using both numerical simulations and an approximate analytical theory we describe a flexoelectric-induced instability in a thin nematic liquid crystal layer with asymmetric boundary conditions subjected to an applied electric field. The dependence of the threshold value of the electric field on principal material parameters of the nematic liquid crystal and the director distribution in different regions of the cell have been studied in detail numerically. The results have been compared with a simple analytical theory that enables us to obtain explicit expressions for the threshold electric field and the period of modulation above the threshold. It has been found that in the hybrid aligned nematic cell with homeotropic anchoring on one surface and planar homogeneous anchoring on the other surface, a periodic flexoelectric-induced domain structure appears, above a critical threshold, with a chiral director distribution. The director rotates about the alignment axis when moving along a perpendicular direction in the plane of the cell. The absolute value of the threshold field has been found to depend on the direction of the field due to the initial symmetry of the hybrid aligned cell and the presence of flexoelectricity.

Theoretical analysis of the magnetic Fréedericksz transition in the presence of flexoelectricity and ionic contamination.

We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fréedericksz transition H=H{c} . The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/H{c}=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.

Control of the nematic-isotropic phase transition by an electric field.

We use a relatively simple continuum model to investigate the effects of dielectric inhomogeneity within confined liquid-crystal cells. Specifically, we consider, in planar, cylindrical, and spherical geometries, the stability of a nematic-isotropic interface subject to an applied voltage when the nematic liquid crystal has a positive dielectric anisotropy. Depending on the magnitude of this voltage, the temperature, and the geometry of the cell, the nematic region may shrink until the material is completely isotropic within the cell, grow until the nematic phase fills the cell, or, in certain geometries, coexist with the isotropic phase. For planar geometry, no coexistence is found, but we are able to give analytical expressions for the critical voltage for an electric-field-induced phase transition as well as the critical wetting layer thickness for arbitrary applied voltage. In cells with cylindrical and spherical geometries, however, locally stable nematic-isotropic coexistence is predicted, the thickness of the nematic region being controllable by alteration of the applied voltage.

Pulsed addressing of a dual-frequency nematic liquid crystal.

A continuum theory of dielectric relaxation within liquid crystal materials is described and used to model the response of dual frequency materials to single pulse voltage waveforms. The equations governing the anisotropic axis (director) angle, electric field, and induced polarizations are solved numerically to investigate pulsed addressing of a model zenithally bistable liquid crystal device. By suitably tailoring the voltage pulse, it is found to be possible to switch between both bistable states. For short pulses the high frequency components of the leading edge of the voltage pulse excites the perpendicular polarization and forces the director to lie parallel to the cell substrates. For longer voltage pulses the constant dc component of the voltage pulse excites the parallel polarization causing the director to lie perpendicular to the substrates. It is also found that reducing rotational viscosity and increasing the achievable dielectric anisotropies (particularly the high frequency value) can significantly reduce the operating voltages of such a device.

Theoretical model of the transition between C1 and C2 chevron structures in smectic liquid crystals.

We present a study of the effect of weak anchoring on the transition between C1 and C2 chevron structures in smectic-C liquid crystals. The coexistence of C1 and C2 chevron structures within a single cell causes zigzag defects to occur and may affect the optical characteristics of the cell. By standard Euler-Lagrange minimisation of the total energy of the system, we obtain analytical expressions for the equilibrium director cone angle in the two chevron states. These in turn allow us to compare the total energies of the states and determine the globally stable chevron profile. We show that analytical predictions for the critical transition temperature, which depends on anchoring strength and pretilt angle, are in good agreement with those obtained numerically.

Influence of flexoelectricity above the nematic Fréedericksz transition.

Continuum theory is used to demonstrate that the presence of flexoelectricity significantly alters the response to an applied voltage of a homogeneous nematic liquid crystal cell above the ac Fréedericksz threshold voltage. In such a system there is a fitting degeneracy: we obtain very good fits between theory and experimental permittivity data using any value of the sum of flexoelectric coefficients, e(11)+e(33), between 0.0 C/m and 1.5 x 10(-11) C/m. The corresponding values of the nematic bend elastic constant show an inverse parabolic relationship with e(11)+e(33), with K33 being reduced down to 90% of its value when flexoelectricity is neglected.

Flexoelectric switching in a bistable nematic device.

We present a continuum theory model of switching in a bistable nematic liquid crystal device. The bistability of the device investigated relies on the fact that one of the cell surfaces exhibits two stable anchoring states, that is, two surface director orientations are locally stable. Since the other surface exhibits monostable, homeotropic anchoring there are two possible ground state director orientations within the cell, depending on the director orientation at the bistable surface. We first investigate the stability of these base states and find a critical surface anchoring strength below which only one of the states is stable. We also investigate the process of switching between the two stable states through the application of an electric field and the presence of a flexoelectric polarization. At high field strengths the dielectric interaction with the applied field will dominate the flexoelectric effect and may hinder switching. We find, therefore, that a window of possible field strengths exists within which switching occurs.

Biaxial modeling of the structure of the chevron interface in smectic liquid crystals.

We have included the inherent molecular biaxiality of the smectic C phase in a model of the chevron structure. This molecular biaxiality is related to a hindered rotation about the molecular long axis which for chiral, polar molecules induces a spontaneous polarization. Through the coupling between biaxiality and the smectic cone angle, continuity of the molecular distribution at the chevron interface leads to changes in the cone angle. Under certain approximations we are able to find analytic expressions for the chevron structure and consequently estimate the width of the chevron interface. There are in fact two correlation lengths which govern variations in the cone angle and the biaxiality.