Bend Distortion Research Articles

The Casimir-like effect induced by active nematics

We consider an active nematic phase and use hydrodynamical equations of it to model the activity as an internal field. The interaction of this field with the nematic director in a confined geometry is included in the Hamiltonian of the system. Based on this model Hamiltonian and the standard field theoretical approach, the Casimir-like force induced between the boundaries of such a confined film is discussed. The force depends on the geometrical shape and the dynamical character of the constituents of our active phase, as well as the anchoring conditions. For homeotropically aligned rod-like particles which in principle tend to align along a planar flow field, extensile activity enhances the attraction present in a thin nematic film. As the film thickness increases the force reduces. Beyond a critical thickness, a planar flow field instantaneous to a bend distortion sets in. Near but below the threshold of this activity-induced instability, the force crosses zero and repulsively diverges right at the critical threshold of this so-called flow instability. For contractile rods, in the same geometry as above, the structure is stable and the Casimir-like force diminishes by an exponential factor as a function of the film thickness. On the other side for a planar director alignment, rod-like contractile particles can induce opposite shear flows at the boundaries creating a splay distortion for the director between the plates. In this configuration, we obtain the same universal pretransitional behavior for the force as above. Vice versa, for extensile rod-like particles in this geometry, the director fluctuations become massive and the Casimir-like force diminishes again by an exponential factor as the film thickness increases. The effect of the active field on thermal fluctuations of the director and the fluctuation-induced Casimir force per area is derived through a "semi"-dynamical approach as well. However, the results of the calculation due to a mathematical sum over the fluctuating modes do not lead to an approved closed form.

Melted grain boundaries in smectic A under imposed bend: role of the anisotropy

ABSTRACT The well-known de Gennes analogy between smectics and superconductors predicts two types of smectic A behaviour under imposed bend. In Type I smectics, the smectic order melts, expelling all of the bend in a bulk nematic region (3D ‘defect’). In Type II smectics, the order melts on 1D defects, edge dislocation lines, which form an Abrikosov-like lattice. Here, I discuss how the strong anisotropy of the smectic coherence lengths influence the smectic A behaviour under imposed bend distortion. I show analytically and numerically that, as proposed previously, a third type of behaviour is possible close to a second-order nematic–smectic A transition, with smectic order melting on the plane of the grain boundary (2D defects). This third kind of behaviour, Melted Grain Boundary (MGB), which has been previously reported experimentally in the smectic A material 9CB, is intermediate between the Type I and Type II behaviours and can be considered as Type ‘one-and-a-half’ smectic A. I define the domain of material parameters in which the planar MGB defect is energetically and topologically stable. I discuss also if similar planar defects may exist, or not, in other anisotropic materials, e.g. superconductors, chiral smectic A, cholesterics and twist-bend nematics.

Magnetic field-induced Freedericksz transition in a chiral liquid crystal

A wedge cell made of homeotropically treated glass plates is filled with a chirally doped nematic liquid crystal. When a sufficiently large magnetic field is applied in the cell plane, a bend-like distortion occurs above a Fréedericksz threshold field Hth. Hth is reduced from the achiral case because of a field-induced bend distortion that facilitates a chiral twist distortion. Measurements of Hth vs sample thickness are reported and compared favorably with a theoretical model presented herein. A further theoretical comparison is made between Hth and the electric-field-induced transition in a geometry, exhibiting a 2π azimuthal degeneracy. The results may have technological implications in, for example, in-plane switching devices.

Catapulting of topological defects through elasticity bands in active nematics.

Active materials are those in which individual, uncoordinated local stresses drive the material out of equilibrium on a global scale. Examples of such assemblies can be seen across scales from schools of fish to the cellular cytoskeleton and underpin many important biological processes. Synthetic experiments that recapitulate the essential features of such active systems have been the object of study for decades as their simple rules allow us to elucidate the physical underpinnings of collective motion. One system of particular interest has been active nematic liquid crystals (LCs). Because of their well understood passive physics, LCs provide a rich platform to interrogate the effects of active stress. The flows and steady state structures that emerge in an active LCs have been understood to result from a competition between nematic elasticity and the local activity. However most investigations of such phenomena consider only the magnitude of the elastic resistance and not its peculiarities. Here we investigate a nematic liquid crystal and selectively change the ratio of the material's splay and bend elasticities. We show that increases in the nematic's bend elasticity specifically drives the material into an exotic steady state where elongated regions of acute bend distortion or "elasticity bands" dominate the structure and dynamics. We show that these bands strongly influence defect dynamics, including the rapid motion or "catapulting" along the disintegration of one of these bands thus converting bend distortion into defect transport. Thus, we report a novel dynamical state resultant from the competition between nematic elasticity and active stress.

Field-induced oblique helicoidal cholesteric phases in mixtures of chiral and achiral liquid crystalline molecules

ABSTRACTWe present a mean field theory to describe phase transitions in mixtures of chiral and achiral liquid crystalline molecules in the presence of an external field. When a longitudinal external field is applied parallel to the pitch axis of a chiral nematic phase (N*), the director of the N* phase can lead to an oblique heliconical cholesteric () state with a twist–bend distortion, in which a bend elastic constant is smaller than a twist elastic constant . We predict that the exists between N* and nematic (N) phases and can be controlled by temperature and concentration. We find various phase transitions: the first-order (isotropic) and the second-order , transitions, on the temperature–concentration plane. We also predict the pitch and the phase diagrams, depending on temperature and concentration under the external field.

Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal.

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant K. The magnitude of K is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼106 Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the "pseudo-layer" structure of the TB phase with Beff in the range 103-104 Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director.

Measurement Method for Flexoelectric Coefficients of Nematic Liquid Crystals by Means of Symmetrically Oblique Incidence Transmission Ellipsometry

Improved measurement method for the flexoelectric coefficients of nematic liquid crystal based on the renormalized transmission ellipsometry is demonstrated. For eliminating the inaccuracy in the measurement of retardation caused by multiple-beam interference in anisotropic multilayer-structured thin films, symmetrically oblique incidence transmission Ellipsometry (SOITE) has proposed and applied to the determination of the device parameters such as the cell gap, surface anchoring energy, reduced dielectric anisotropy and reduced elastic constant. We applied the SOITE technique to determine the flexoelectric coefficients (e11 + e33) for the splay and bend distortion.

Rectangle Lattice Large Mode Area Photonic Crystal Fiber for 2 $\mu$m Compact High-power Fiber Lasers

A rectangle lattice silica-host photonic crystal fiber with large mode area (LMA) is successfully fabricated for the first time. The introduction of rectangle lattice contributes to distinct leakage of second order modes and two large air holes provide an effective solution to suppress bend distortion. Numerical results demonstrate that a large mode field area (MFA) of 2500 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is achieved at the wavelength of 2 μm when the fiber is straight. While the fiber is bent to a radius of 30 cm, it confirms to single-mode (SM) operation conditions and the decrements of MFA at x polarization and y polarization are just 4.3% and 5%. Within a bend orientation angle of ± 10° and a wide wavelength range from 1.8 μm to 2.4 μm, the fiber can operate under single-mode (SM) conditions with low bend loss. LMA, SM operation, and small bend distortion make this fiber of great potential in developing 2 μm compact high-power fiber lasers.

Semi-Quantitative Risk Assessment Matrix for Rotating Equipment

In petrochemical, power generation, oil and gas industries and in variety of other sectors rotating equipments are in use to fulfill production requirements. Failure of rotating equipment, especially in such industries can result to risk related issues. A well implemented rotating equipment risk assessment strategy is most needed to achieve desired plant availability and efficiency. In this research semi-quantitative risk assessment approach is proposed to evaluate the risk of rotating equipment and categorize their associated failure risks. Borda ranking is adopted to evaluate the risk in order to minimize risk ties which exist in risk matrix. Compressor is taken as case study to show the applicability of the proposed method for rotating equipment. It was observed that risks of selected failure modes of gas turbine compressor fall in the categories of serious and medium levels based on risk matrix. Rotor bend distortion, blade failure or inlet guide vane failures needed more attention for treatment based on Borda ranking.

Bend-resistant large-mode-area photonic crystal fiber with a triangular-core

In view of its feasibility for fabrication and application, a bend-resistant large-mode-area photonic crystal fiber with a triangular core is proposed. In our design, the fiber proposes a solution to the issue of bend distortion. The mode field area of the fundamental mode at the wavelength of 1.064 μm achieves 930 μm² at the straight state and 815 μm² at a bending radius of 30 cm, respectively. The decrement of the mode field area at the bend state is only 12.473% compared to the straight state. Furthermore, when the fiber is bent with a bending radius of 30 cm, numerical results demonstrate that the fiber conforms to single-mode operation conditions and the bending orientation angle can be extended to ±55°. A large mode area at bent state and low sensitivity of bending orientation make the fiber of great potential in high-power fiber lasers.

The Effect of Submarine Pipelines’ Distortion when Original Parameters Are Changed during Laying

The mechanics model about submarine pipelines during installation is based on the theory of geometrical nonlinear great distortion. The U.L method is adopted as solving problem about the contact between submarine pipeline and seabed, the results obtained by this method are equally accurate and less computational work is need when solving pipeline’s non-linear great distortion. According to select different original parameter during laying pipeline, the bend distortion to submarine pipeline is calculated and the effect of bend distortion to submarine pipeline is analyzed.

Defect trajectories in nematic shells: Role of elastic anisotropy and thickness heterogeneity

We introduce the idea of transformation trajectories to describe the evolution of nematic shells in terms of defect locations and director field when the elastic anisotropy and the shell thickness heterogeneity vary. Experiments are compared to numerical results to clarify the exact role played by these two parameters. We demonstrate that heterogeneity in thickness is a result of a symmetry breaking initiated by buoyancy and enhanced by liquid crystal elasticity, and is irrespective of the elastic anisotropy. In contrast, elastic anisotropy--in particular, disfavored bend distortion--drives an asymmetric defect reorganization. These shell states can be both stable or metastable.

Bend Insensitive Design of Large-Mode-Area Microstructured Optical Fibers

Numerical investigation on the design of a novel kind of large-mode-area optical fiber is presented. Low bending loss propagation in the fiber is achieved by the introduction of low-index rods with small period and large normalized diameter in one segment of the cladding. Single-mode operation is realized by the introduction of low-index rods with large period and small normalized diameter in another segment of the cladding. When a conventional large-mode-area optical fiber is bent, it will generally experience large bend distortion and the mode area will reduce accordingly. To avoid that, a bend-resistant design by introducing a microstructure into the solid core of the proposed fiber is proposed. In particular, the mode area of one such fiber is always larger than 2000 μ m2 when the bending radius is larger than 30 cm at the wavelength of 1.064 μm.

Splay bend elasticity of a bent-core nematic liquid crystal

We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a bent-core liquid crystal. In the vicinity of the nematic-isotropic transition temperature K33 is proportional to the square of the order parameter. In the nematic range K11 increases monotonically with decreasing temperature, whereas K33 is practically independent of temperature and is smaller than K11 . K33 exhibits a pretransitional slow divergence toward the transition temperature to the smectic phase and becomes slightly larger than K11. The small K33 is explained on the basis of strong coupling of the bent shape of the molecules with the bend distortion.

Improvement of Coiling Mode to Suppress Higher-Order-Modes by Considering Mode Coupling for Large-Mode-Area Fiber Laser

Mode coupling, bend distortion and bend loss are important considerations in large mode area (LMA) fiber laser. Both mode coupling and mode distortion were studied in the step-index fiber in theory. The dependence of mode power on propagation distance, effective bend radius was calculated with the bend radius changing suddenly and gradually. Taking mode coupling into account, we designed a new cone-shaped coiling device for beam quality improvement. These results and design are of benefit to the applications of coiling fiber to improve beam quality for LMA fiber laser.

应用于弯曲条件下高功率光纤放大器的大模面积稀土掺杂光纤的设计

The numerical study on the performance of large-mode-area (LMA) fibers coiled onto a spool in high power amplifier is carried out as the bend-induced distortion of fiber modes severely affects the output characteristics of amplifier systems. The variations for high-order mode bend distortion with different orientations relative to the plane of the fiber bend are observed and shown. Concerning the practical applications, a bend-resistant LMA fiber with the mode area larger than 1000 \mum2 and excellent high-order mode suppression is designed completely by optimizing the refractive index (RI) and dopant profile. The results indicate that a hybrid profile of RI and dopant is the best choice for LMA fiber with coiling.

Diverging elasticity and director uniformation in a nanopatterned cell near the nematic–smectic-Aphase transition

The stylus of an atomic force microscope is used to scribe herringbone patterns of various wavelengths into a polyimide-coated substrate. The patterns serve as a template for alignment of the liquid crystal octyloxycyanobiphenyl and impose a bend distortion in the liquid crystal in the vicinity of the herringbone apexes. The pretransitional behavior of the liquid crystal is observed by polarized microscopy as it is cooled through the nematic-smectic- A phase transition, facilitating direct visualization of the extrapolation length, which is related to the trade-off between elastic and anchoring forces. Just above the phase transition temperature the expulsion of bend deformation is observed and is shown to be in good quantitative agreement with continuum theory. Very close to the transition temperature a weak threshold behavior is observed, wherein the smectic- A phase forms a monodomain for short period herringbones, but breaks into multiple domains when the patterned period is large.

Anomalous Temperature Dependence of Elastic Constants in the Nematic Phase of Binary Mixtures Made of Rodlike and Bent-Core Molecules

We report on two anomalous trends in the temperature dependences of the splay (K11) and bend (K33) elastic constants in the nematic (N) phase of mixtures of compounds with rodlike (R) and bent-core (BC) molecules: As the sample is cooled from the isotropic to N transition point, (i) K33 increases, attains a maximum value and then decreases, and (ii) close to the N to smectic A (SmA) transition point, K11 decreases sharply. At higher temperatures the bow axes of BC molecules are aligned along the director n, strongly favoring a bend distortion of n as the orientational order parameter is increased. Close to the N-SmA transition point the smecticlike short-range order builds up, and the arrow axes of BC molecules are aligned along n, facilitating a splay distortion of n. A simple model calculation brings out the anomalous trend in K33.

Design of large-mode-area amplifier fibers resistant to bend-induced distortion

As fiber amplifiers and lasers achieve higher power, gain fiber designs are pushing toward extremely large-mode area. In this regime, bend-induced distortion of fiber modes becomes large and can severely impact amplifier performance. Previous results describing bend-induced reduction of effective area are reviewed and extended with a numerical analysis of how bend distortion impacts interaction with the gain. Distortion-resistant designs such as the parabolic fiber are shown to substantially improve gain-interaction indicators as well as all other performance metrics simulated, and are predicted to dramatically outperform step-index fibers.

Intuitive modeling of bend distortion in large-mode-area fibers

Bend distortion is emerging as an important consideration in the design of amplifier fibers with a large mode area, in addition to bend loss and mode-coupling effects. Simple, intuitive estimates of distortion sensitivity are presented for two interesting classes of fibers, in agreement with full numerical simulations.