Electric field effects on nematic wetting layers

We present a theoretical investigation of the temperature and electric field dependence of nematic liquid crystal wetting layers close to an aligning substrate within a confined system. Using a mesoscopic Q tensor theory coupled to Maxwell's equations for the electric field, we consider the existence and stability of homogeneous nematic wetting layers close to the substrate. Numerical results are presented showing the phase diagram for the isotropic (paranematic), nematic and wetting layer states. The effect on the isotropic-wetting transition, from first order to second order, when an electric field is applied is then investigated

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 anti-phase, 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

Flexoelectric polarisation effects in nematic liquid crystal phase gratings

Nematic phase gratings have been studied in which a planar nematic layer of thickness 17.2 μm is sandwiched between two glass substrates coated with an alignment polymer. The upper substrate is a continuous earth plane and the lower substrate has a patterned electrode of interdigitated stripes (electrodes and gaps are both 40 μm wide). Reorientation of the nematic liquid crystal occurs in response to d.c. electric fields applied between the interdigitated electrodes. These nematic reorientation regions have been used to investigate the influence of the flexoelectric polarisation in the nematic liquid crystal by observing the resultant (i) movement of tilt fringes in a Mach-Zehnder interferometer, and (ii) optical diffraction patterns. In the Mach-Zehnder interferometer the periodic variation of the refractive index resulting from the periodic distortion profile is measured directly from the displacement of the tilt fringes. The asymmetry in the response to positive and negative polarities of the d.c. voltage for both measurement techniques is directly related to the sum of the flexoelectric coefficients, e1 + e3

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

Derivative-order-dependent stability and transient behaviour in a predator–prey system of fractional differential equations

In this paper, the static and dynamic behaviour of a fractional-order predator–prey model are studied, where the nonlinear interactions between the two species lead to multiple stable states. As has been found in many previous systems, the stability of such states can be dependent on the fractional order of the time derivative, which is included as a phenomenological model of memory-effects in the predator and prey species. However, what is less well understood is the transient behaviour and dependence of the observed domains of attraction for each stable state on the order of the fractional time derivative. These dependencies are investigated using analytical (for the stability of equilibria) and numerical (for the observed domains of attraction) techniques. Results reveal far richer dynamics compared to the integer-order model. We conclude that, as well as the species and controllable parameters, the memory effect of the species will play a role in the observed behaviour of the system

Molecular simulation of chevrons in confined smectic liquid crystals

Chevron structures adopted by confined smectic liquid crystals are investigated via molecular dynamics simulations of the Gay-Berne model. The chevrons are formed by quenching nematic films confined between aligning planar substrates whose easy axes have opposing azimuthal components. When the substrates are perfectly smooth, the chevron formed migrates rapidly towards one of the confining walls to yield a tilted layer structure. However, when substrate roughness is included, by introducing a small-amplitude modulation to the particle- substrate interaction well-depth, a symmetric chevron is formed which remains stable over sufficiently long runtimes for detailed structural information, such as the relevant order parameters and director orien- tation, to be determined. For both smooth and rough boundaries, the smectic order parameter remains non-zero across the entire chevron, implying that layer identity is maintained across the chevron tip. Also, when the surface-stabilised chevron does eventually revert to a tilted layer structure, it does so via surface slippage, such that layer integrity is maintained throughout the chevron to tilted layer relaxation process. </p

The composition of the protosolar disk and the formation conditions for comets

Conditions in the protosolar nebula have left their mark in the composition of cometary volatiles, thought to be some of the most pristine material in the solar system. Cometary compositions represent the end point of processing that began in the parent molecular cloud core and continued through the collapse of that core to form the protosun and the solar nebula, and finally during the evolution of the solar nebula itself as the cometary bodies were accreting. Disentangling the effects of the various epochs on the final composition of a comet is complicated. But comets are not the only source of information about the solar nebula. Protostellar disks around young stars similar to the protosun provide a way of investigating the evolution of disks similar to the solar nebula while they are in the process of evolving to form their own solar systems. In this way we can learn about the physical and chemical conditions under which comets formed, and about the types of dynamical processing that shaped the solar system we see today. This paper summarizes some recent contributions to our understanding of both cometary volatiles and the composition, structure and evolution of protostellar disks.Comment: To appear in Space Science Reviews. The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-015-0167-

Order parameter theory of the pre-transitional behaviour in antiferroelectric liquid crystals

We propose anorder parameter theoryas a possible description of the pre-switching behaviour of antiferroelectric liquid crystals (AFLCs). Assuming that the antiferroelectric state is preserved so that the directors in adjacent layers are on opposite sides of the smectic cone, we consider changes in the molecular order about these directors. Our theory incorporates interlayer and intralayer dipole-dipole interactions, the dipole-electric field interaction and the thermodynamic potential. The effective optic axis as a function of applied voltage can then be calculated and is found to be in qualitative agreement with experimental observations which show a superlinear dependence

In-layer defects in smectic C materials

We investigate the director structure close to the core region of in-layer defects found in smectic C thin films. These defects are similar to nematic disclination lines in appearance and we use the Landau-de Gennes formulation for the free energy of the system previously used to consider nematic defects. The minimum energy core structures are numerically calculated and two possible structures found, where either a standard smectic A or a de Vries smectic state is formed at the centre of the defect. These two states correspond to the escaped and planar configurations of nematic disclination cores. Finally, the energies of these core structures are found as functions of the dimensions of the thin film

Liquid crystal theory and modelling

In this chapter we explain the rationale behind the theoretical modeling of liquid crystals and explain the important steps to construct a realistic and accurate model for a particular physical system. We then summarize two commonly used theories of nematics: one based on using the director as a dependent variable and one based on using the tensor order parameter. Using an example problem, the π-cell, we show the advantages and disadvantages of these two theoretical approaches, demonstrating the importance of carefully considering the choice of model before embarking on simulations