Analysis of Off-Axial Optical Systems (2)

The extended 4×4 Gaussian bracket matrix Gij represents the lowest order quantity of “aberration coefficient tensor quantities” which are defined to as the peculiarity of off-axial optical systems and are independent of azimuths. We newly confirmed this extended 4×4 Gaussian bracket matrix of deflection (refraction or reflection), transmission and “twisting.” The result determined by use of a new representative method of asymmetrical surfaces and a method of paraxial expansion along the folded reference axis shows that the 4×4 Gaussian bracket matrix is the extended form of the 2x2 Gaussian bracket matrix which is used in co-axial rotational symmetric optical systems. Furthermore, we analyze and formalize the crossterm effects, which are the most serious problem in optical systems having multiple off-axial surfaces, using the concept of a chain of “optical systems divided into former and latter” and the vector-tensor analysis method. The result of this analysis reveals the structure of the cross-term effects and proves the usefulness of the vector-tensor analysis method in general image analysis.     

Tuning helical twisting power and photoisomerisation kinetics of axially chiral cyclic azobenzene dopants in cholesteric liquid crystals

ABSTRACT

Significant attention has been paid to improve the helical twisting power (β) and Δβ between the two different isomers of axially chiral azobenzene dopants in cholesteric liquid crystals (CLCs); however, the correlations between the vales (β and Δβ) with the molecular structures as well as photoisomerisation kinetics are far from clear. In this study, a series of binaphthyl-azobenzene cyclic dopants R1–R3 with different lengths of alkoxy chain was synthesised, which exhibited photochemically reversible trans–cis isomerisation in both organic solvents and liquid crystal hosts. When doping into a nematic liquid crystal, dopant R2 with one linking alkoxy group showed the highest values of β and Δβ. The results revealed that the β value was related to the dihedral angle between two naphthyl planes and the miscibility between the dopants and the host molecule. Moreover, Δβ was also depended on the photoisomerisation quantum yields. With increasing length of alkoxyl chain, the photoisomerisation rate constant of dopants increased upon ultraviolet irradiation and decreased for the reverse process upon visible light irradiation either in isotropic acetonitrile or in CLCs. These results enable the precise tuning of the pitch and selective reflection wavelength of CLCs.     

A DAMAGE MECHANICS MODEL FOR TWISTED CARBON NANOTUBE FIBERS

Carbon nanotube fibers can be fabricated by the chemical vapor deposition spinning process. They are promising for a wide range of applications such as the building blocks of high-performance composite materials and micro-electrochemical sensors. Mechanical twisting is an effective means of enhancing the mechanical properties of carbon nanotube fibers during fabrication or by post processing. However, the effects of twisting on the mechanical properties remain an unsolved issue. In this paper, we present a two-scale damage mechanics model to quantitatively investigate the effects of twisting on the mechanical properties of carbon nanotube fibers. The numerical results demonstrate that the developed damage mechanics model can effectively describe the elastic and the plastic-like behaviors of carbon nanotube fibers during the tension process. A definite range of twisting which can effectively enhance the mechanical properties of carbon nanotube fiber is given. The results can be used to guide the mechanical twisting of carbon nanotube fibers to improve their properties and help optimize the mechanical performance of carbon nanotube-based materials.     

Chordal Coxeter groups

A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every cycle of length at least four has a chord. As an application, we construct counterexamples to two conjectures concerning the isomorphism problem for Coxeter groups.      

Resonant spin-flavor precession constraints on the neutrino parameters and the twisting structure of the solar magnetic fields from the solar neutrino data

Resonant spin-flavor precession (RSFP) scenario with twisting solar magnetic fields has been confronted with the solar neutrino data from various ongoing experiments. The anticorrelation apparent in the Homestake solar neutrino data has been taken seriously to constrain (Δ m ² ,φ′) parameter space and the twisting profiles of the magnetic field in the convective zone of the Sun. The twisting profiles, thus derived, have been used to calculate the variation of the neutrino detection rates with the solar magnetic activity for the Homestake, Super-Kamiokande and the gallium experiments. It is found that the presence of twisting reduces the degree of anticorrelation in all the solar neutrino experiments. However, the anticorrelation in the Homestake experiment is expected to be more pronounced in this scenario. Moreover, the anticorrelation of the solar neutrino flux emerging from the southern solar hemisphere is expected to be stronger than that for the neutrinos emerging from the northern solar hemispheres.     

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.     

Sign Reversal of a Large Circularly Polarized Luminescence Signal by the Twisting Motion of a Bidentate Ligand

This work demonstrates sign reversal of large circularly polarized luminescence (CPL) signal based on the hinge‐like twisting motion of a bidentate ligand, 3,3‐bis(diphenylphosphoryl)‐2,2‐bipyridine (BIPYPO), in a cis–trans isomerization of chiral europium(III) complexes. X‐ray diffraction analysis revealed that twisting motion of BIPYPO provides s‐cis and s‐trans geometries of a chiral Eu^III complex containing either tris[3‐(trifluoromethylhydroxymethylene)‐(+)‐camphorate] (D ‐ 1 ) or tris[3‐(heptafluoropropylhydroxymethylene)‐(+)‐camphorate] (D ‐ 2 ). The s‐cis Eu^III complexes show eight‐coordinate geometry around the Eu^III ion, in which the chelate between the phosphoryl oxygen and the Eu^III ion forces the s‐cis geometry of BIPYPO. In contrast, the phosphorus–nitrogen interaction provides a conformational lock for the s‐trans geometry of the BIPYPO ligand, inducing a quasi‐seven‐coordinate Eu^III complex. The difference in coordination geometry causes the sign change of the CPL signals between the s‐cis and s‐trans isomers, whereby the s‐cis and s‐trans isomers of Eu^III complexes exhibit the positive and negative CPL signals, respectively, for the ⁵D₀→⁷F₁ transition. The proportion of the s‐trans‐D ‐ 1 against s‐cis‐D ‐ 1 increases upon changing the solvent from [D₃]acetonitrile to [D₆]acetone, inducing a sign change of the CPL signals. The complexes D ‐ 1 and D ‐ 2 show a biexponential decay with two different lifetimes, suggesting two emitting species, that is, the s‐cis and s‐trans isomers of Eu^III complexes. In both cases, the proportions of the longer lifetime components (τ₁) decrease and instead the shorter lifetime components (τ₂) increase upon changing the solvent from [D₃]acetonitrile to [D₆]acetone.     

Derivatives of menthothiophene as chiral dopants for nematic liquid crystals

New chiral derivatives of thiophene fused with menthane, camphor or the 3R-3-methylcyclohexane ring were prepared and studied as chiral dopants in cholesteric liquid crystalline mixtures. The helical twisting power of the most effective compounds of this series, menthothiophenes, was strong enough to obtain selective reflection of visible light at 16 wt% concentration of the dopant in a non-chiral nematic host.     

Kojic acid—a new fragment for the preparation of bent‐core mesogens

Kojic acid was used to synthesize bent‐core mesogens. Antiferroelectric polar smectic mesophases, an oblique and a rectangular columnar mesophase were found. The mesophases were characterized by X‐ray scattering, electro‐optical measurements, polarizing microscopy and DSC. On the base of these measurements, models of the mesophases are proposed.     

Bent‐shaped liquid crystals containing a furan bridge in the mesogenic core

We report the synthesis and characterization of hitherto unreported bent‐shaped dimeric liquid crystals based on a furan bridge in the mesogenic core. The compound 18‐Fu2 exhibits liquid crystalline behaviour.