Inverse Pitch Research Articles

On the superposition of multipolar spherical and cylindrical oscillations in swirling rigid flow

It is shown that a superposition of an arbitrary number of multipolar spherical and cylindrical oscillations in a cylindrical rigid flow with swirl is an exact solution to the time-dependent nonlinear vorticity equation. The oscillations are normal modes whose fundamental frequency and radial wavenumber are given by the angular speed and scaled inverse pitch, respectively, of the rigid flow.

Statistical Theory of Helical Twisting in Nematic Liquid Crystals Doped with Chiral Nanoparticles

A molecular field theory of the cholesteric ordering in nematic nanocomposites doped with chiral nanoparticles was developed taking into consideration chiral dispersion interaction between rod-like nanoparticles. It was shown that the inverse pitch of the cholesteric helical structure is proportional to the anisotropy of the effective polarizability and the anisotropy of the effective gyration tensor of a nanoparticle in the nematic host. The theory enables one to predict the helical sense inversion induced by a change of the low-frequency dielectric susceptibility of the nematic host phase. The components of the high-frequency effective polarizability and the effective optical activity of a gold rod-like nanoparticle in a particular nematic solvent were calculated numerically.

A chiral-racemic lyotropic chromonic liquid crystal system.

The two main classes of liquid crystals are thermotropic (containing no solvent) and lyotropic (containing solvent). Both of these classes possess the nematic phase, the most simple of liquid crystal phases with only uniaxial orientational order. For both of these classes, if the constituent molecules are chiral or if a chiral dopant is added, the preferred direction of orientation rotates in helical fashion in what is called the chiral nematic phase. Recent research has shown that because the ordering entities of the two classes are quite different (molecules versus molecular assemblies), important differences in the properties of the nematic phase can result. While thermotropic chiral nematics have been extensively examined, less is known about lyotropic chiral nematics, especially for the most ideal case, a chiral-racemic system. Furthermore, none of the lyotropic chiral-racemic studies has included lyotropic chromonic liquid crystals, which are solutions of dyes, drugs, and nucleic acids. Inverse pitch measurements are reported for a chiral-racemic system of a chromonic liquid crystal across the entire chiral fraction range and over a 30 °C temperature interval. The inverse pitch depends linearly on chiral fraction and decreases with increasing temperature, indicating that achiral and chiral molecules participate in the assembly structure similarly. The helical twisting power is significantly larger than for other chiral lyotropic liquid crystals due to the very high scission energy of the investigated system.

Pitch measurements in chiral lyotropic chromonic liquid crystals

ABSTRACTThe recent interest in lyotropic chromonic liquid crystals (LCLCs) has resulted in significant understanding of the assembly behaviour and liquid crystal properties of these water-based systems. On the other hand, there has been much less investigation into chiral LCLCs, which result if the chromonic molecule is chiral or if a chiral dopant is added to the solution. Measurements of the pitch of the LCLC disodium cromoglycate (DSCG) with several chiral dopants using both the Cano wedge and fingerprint texture methods are reported. The results include quantitative measurements of both the pitch and the helical twisting power. The ability of dopants to induce twist in DSCG varies widely, with some having almost no effect, with others producing a pitch approaching 3 and with most displaying an inverse pitch–dopant concentration dependence that is nonlinear at high concentrations.

Reflectivity of cholesteric liquid crystals with spatially varying pitch.

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.

Viscoelastic modes in chiral liquid crystals

Viscoelastic properties of liquid crystals are very important for applications like display technology. However, there are not many direct techniques to study them. In this review, we describe our studies on the viscoelastic modes of some chiral liquid crystals using dynamic light scattering. We discuss viscoelastic modes corresponding to the C director fluctuations in the chiral smectic C phase and the behaviour of the Goldstone-mode near the chiral smectic C-smectic A phase transition. In cholesteric liquid crystals, we consider the director fluctuations in a wavevector range comparable to the inverse pitch of the cholesteric. Here, the study of the scattered light in the vicinity of the Bragg reflection using a novel geometry will be presented.

A dynamic light scattering study of the viscoelastic twist mode in cholesteric liquid crystals

Although viscoelastic properties of liquid crystals are very important for applications like display technology, there are not many direct techniques to study them. We have used dynamic light scattering to obtain dispersion curves for the twist mode of director fluctuations in a thermotropic cholesteric liquid crystal (cholesteric) mixture, in a wave vector range comparable to the inverse pitch of the cholesteric. In the experiment, light scattered in the vicinity of Bragg reflection is investigated using a hitherto unused scattering geometry where the scattering wave vector q is parallel to the cholesteric helix axis. By fitting the experimental data to a parabolic function of the scattering wave vector, we have determined the twist viscoelastic coefficient k 22/γ 1. We have studied the temperature dependence of k 22/γ 1 and found that the viscoelastic coefficient increases rapidly as the cholesteric-to-isotropic transition temperature is approached.

Towards Radiation‐Sensitive Quasi‐Biological Display

The pitch of the columnar cholesteric mesophase formed by the dinucleoside phosphate d(GpG) and water becomes shorter after exposure to γ radiation. This effect can be measured directly with an optical microscope from the distance between the fingerprint lines. The inverse pitch is linearly correlated to the dose absorbed between 0 and 20 kGy.

On chirality induction in lyotropic nematic liquid crystals

Abstract The induction of lyotropic chiral phases by different, structurally related α-hydroxy carboxylic acids as well as the corresponding potassium salts has revealed a distinct dependence of their helical twisting power upon their molecular structure. Obviously there is an effect of the mean electronic polarizability of the moiety neighbouring the chiral centre of the dopant, similar to that in the case of thermotropic induced chiral phases. A significantly non-linear dependence of the inverse pitch on the concentration has been found and is explained as a micelle size effect. The absolute value of the helical twisting power decreases if instead of a chiral acid, the corresponding potassium salt is used to induce the phase chirality; moreover, the handedness of the twist is inverted. A microscopic model for the evolution of chirality in a micellar phase is proposed.

Pitch-induced transition of chiral nematic liquid crystals in submicrometer cylindrical cavities.

A structural transition in the nematic liquid crystal 4'-pentyl-4-cyanobiphenyl (5CB-\ensuremath{\beta}${\mathrm{d}}_{2}$) doped with chiral agents CB15 and CE2, confined to submicrometer cylindrical cavities of alumina membranes, is detected by deuterium nuclear magnetic resonance ${(}^{2}$H NMR). These cavities have radii R of 0.1 \ensuremath{\mu}m and give tangential anchoring conditions. The $^{2}\mathrm{H}$ NMR spectra reveal a transition from a radially twisted to an axially twisted structure. The radially twisted structure is stable for pitch lengths greater than approximately 1 \ensuremath{\mu}m and the axially twisted structure for smaller pitch lengths. For the case of equal bulk elastic constants ${\mathit{K}}_{11}$, ${\mathit{K}}_{22}$, and ${\mathit{K}}_{33}$ the dependence of the Frank free energy on the inverse pitch parameter q, saddle-splay elastic constant ${\mathit{K}}_{24}$, and the surface anchoring strength ${\mathit{W}}_{\mathrm{\ensuremath{\theta}}}$ is studied. In the radially twisted structure the free energy as a function of q has a sawtooth shape for fixed ${\mathit{K}}_{24}$. The phase diagrams showing the stability of the two phases in the inverse twist versus anchoring space for different values of ${\mathit{K}}_{24}$, are calculated. In the weak anchoring regime (${\mathit{RW}}_{\mathrm{\ensuremath{\theta}}}$/K1), a periodic reentrance from axially to radially twisted structures is predicted upon increasing qR. A comparison of theoretical and experimental results in this chiral nematic material yields a ${\mathit{K}}_{24}$ value nearly an order of magnitude smaller than that found in nonchiral nematic phases.

The Homeotropic Surface Anchoring Effects on the C-H Phase Transition

Two simple models are introduced to explane the homeotropic surface anchoring effects on the cholesteric to homeotropic (C-H) phase transition in the absence of an applied field. The calculations are extended to include the effect of an external field perpendicular to the surfaces. The results predict the C-H phase transition with analytical expressions involving the product of cell thickness and inverse pitch.

Relaxation Modes and Visco-Elastic Properties in an Antiferroelectric Liquid Crystal (R)-MHPOBC Observed by Photon-Correlation Spectroscopy

Photon-correlation spectroscopy was performed to observe relaxation modes in an antiferroelectric liquid crystal (R)-MHPOBC. A phase mode in the SmI A * phase, which is the same as one in the incommensurate phase of solid, was observed for the first time. From the dispersion relations of the Goldstone modes in the SmC γ * and SmC A * phases, the ratios of orientational elastic constants to the viscosity coefficient were obtained as a function of temperature. A linear temperature dependence of the inverse pitch in the SmC A * phase was also found, which was discussed on the basis of the phenomenological theory.

Induced circular dichroism from cholesteric polypeptide films doped with an azobenzene derivative

Poly(γ-benzyl L-glutamate-co-γ-dodecyl L-glutamate) doped with an azobenzene derivative was studied. Optimum conditions for the induced circular dichroism (ICD) intensity were explored by varying the cholesteric pitch of the film and the content of the dodecyl groups x. The cholesteric pitch was varied by changing the annealing temperature of the film. The strongest ICD was observed when the polymer with x=0.63 was annealed at 180°C (cholesteric pitch= 6.7 μm). The ICd intensity vs inverse pitch plot was compared with theoretical curves calculated on the basis of Chandrasekhar's theory

The Effect of Homeotropic Surface Anchoring on the Critical Voltage for Unwinding the Cholesteric Phase

Abstract Experimental data are presented for the unwinding of the helical cholesteric structure in the presence of an applied electric field. Homeotropic surface anchoring conditions are known to reduce the magnitude of the critical unwinding voltage which depends on helical pitch and cell thickness. The experiments are unique in that the pitch is varied continuously at constant cell thickness rather than changing thickness at constant pitch. This is accomplished by employing cholesteric mixtures in which the inverse pitch changes linearly with temperature in the nematic compensation region. A model introduced by Cladis and Klemen, and extended by Goossens, is used to explain the effect of surface anchoring in the absence of an applied field. The calculations are extended to include the effect of the field, and the theory predicts a universal critical voltage curve involving the product of cell thickness and inverse pitch which is verified by experiment.

New induced cholesteric micellar liquid crystals. Characterization and pitch determination

New induced cholesteric micellar liquid crystals have been prepared based on potassium laurate and sodium decyl sulfate. The chiral molecule D-glucose was used as dopant. The inverse pitch length is found to be proportional to the added guest. The twist induced by the dopant strongly depends on the nature of the detergent, the principal component of the mesophases. The mesophases are characterized on the basis of the microscopic textures. Deuterium NMR spectra in D2O shows positive diamagnetic anisotropy for these cholesteric mesophases.

Dependence of spontaneous polarization, rotational viscosity and helical pitch of smectic c* compounds on the enantiomeric excess

Abstract We report on investigations of three distinct pure SC* compounds for which we measured the dependence of the spontaneous polarization, the rotational viscosity, and the SC*-pitch on enantiomeric excess. The quantities under consideration partly exhibit non-linear behaviour. A simple statistical model is proposed that accounts for both linear and non-linear dopant concentation dependencies of the spontaneous polarization. The rotational viscosity with respect to the ĉ-director increases with increasing spontaneous polarization. The inverse pitch, z−1, exhibits a strongly non-linear behaviour for small concentrations, however, we do not observe a sharp threshold concentration below which no helix exists. Some practical consequences of our findings are discussed.

Topology of a Surface of the Phase Diagram of the Cholesteric Lyotropic Mesophase: Potassium Laurate/1-Decanol/Water/I-N-Lauroyl Potassium Alaninate

Abstract A surface of the phase diagram of the lyotropic cholesteric mesophase of potassium laurate/1-decanol/H2O/l-N-lauroyl potassium alaninate (l-LAK) is studied by optical microscopy and X-ray diffraction as a function of the relative molar concentration of l-LAK and temperature. Cholesteric discotic and calamitic phases are observed and also a large domain of biaxial cholesteric phase. The inverse pitch as a function of the l-LAK relative molar concentration presents a linear behavior in the doping range studied. The l-LAK doping and its influence in favoring cholesteric calamitic phase formation are discussed in terms of the packing of the l-LAK amphiphile in the bilayer and the orientational fluctuations of the intrinsically biaxial correlation volumes.

Copolyesters exhibiting a thermotropic cholesteric phase

AbstractMesomorphic copolymers were synthesized by incorporating varying ratios of azelaic acid and (+)‐3‐methyl adipic acid into copolyesters based upon 4,4′‐dihydroxybiphenyl. Introduction of the phenylene (+)‐3‐methyl adipate unit broadens the temperature range of the nematic phase of the azelate homopolymer and, at the same time, produces a chiral nematic (cholesteric) mesophase which exhibits various iridescent colors. Circular dichroism measurements were used to determine the pitch of the cholesteric liquid crystals. The pitch decreased gradually with increasing temperature, and the inverse pitch increased in direct proportion to the molar content of the units containing (+)‐3‐methyl adipate. The twisted cholesteric structure could be conserved by quenching to produce films with various colors at room temperature. Annealing these films at a temperature immediately below that of the crystal–mesophase transition improved the regularity of the cholesteric structure.

Helical pitch in mixtures of cholesteric liquid crystals

The behavior of the helical pitch in binary mixtures of cholesteric liquid crystals is studied by means of a simple molecular model (an extension to mixtures of a model introduced by Priest and Lubensky). The model exhibits helical inversion, and with some reasonable assumptions is shown to be capable of giving order of magnitude agreement with experiments performed by Baessler and Labes. It is found that helical inversion is driven by the variation with temperature of the nematic order parameters of the two components of the mixture. A general argument is given for the linearity of inverse pitch wavenumber versus concentration difference in the special case of a mixture of the left- and right-handed versions of a single cholesteric liquid crystal. (Such a system was studied experimentally by Dolphin et al.)