Bend Elastic Constants Research Articles

Effects of quantum dots on the nematic to smectic-A phase transition

ABSTRACT Experiments on the composites of liquid crystals and quantum dots showed the significant role of quantum dots on the properties of the nematic–smectic-A phase transition. The effects of quantum dots on the nematic-smectic-A phase transition have been discussed using Flory- Huggins theory of isotropic mixing and Landau-de Gennes theory. The impact of quantum dots on the smectic-A order parameters, nematic–smectic-A transition temperature, splay and bend elastic constants has been discussed. The smectic-A order parameters, transition temperature and elastic constants decrease with the increase of volume fraction of quantum dots.

Cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase: on the role played by the length and parity of the spacer

ABSTRACT Six members of the 1,ω-bis(4-cyanobiphenyl-4′-yl) alkanes are reported and referred to as CBnCB in which n = 1, 15, 16, 17, 19 and 20 and indicates the number of methylene units in the spacer separating the two cyanobiphenyl units. The behaviour of CB3CB is revisited. The temperature dependence of the refractive indices, optical birefringence and dielectric permittivities measured in the nematic, N, phase for selected homologues are reported. The dimers with n ≥ 15 showed an enantiotropic N phase, and for the odd members the twist-bend nematic, NTB, phase was observed. CB3CB shows a direct NTB-isotropic, I, transition, whereas for CB1CB a virtual NTB-I transition is found. The temperature dependence of the bend elastic constant, K 33 , measured in the oblique helicoidal cholesteric state formed by mixtures of CBnCB with a chiral additive S811, shows strong non-monotonous behaviour with a deep minimum near the transition point to the NTB phase. The minimum value of K 33 decreases as n increases. The long even members of the CBnCB series show similar values of TNI to their odd-membered counterparts, but their estimated values of TNTB N are considerably lower. This is attributed to molecular shape and its effect on K 33 .

Emergent gauge symmetry in active Brownian matter.

We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).

Theoretical models for the nematic twist-bend phase and the Landau de Gennes theory of Longa and Tomczyk

ABSTRACT We present a critical analysis of the existing phenomenological theories of the nematic twist-bend phase including the models proposed by Dozov and Selinger and the more general Landau de Gennes theory of L. Longa and W. Tomczyk. The role of the flexoelectric polarisation is considered in detail as well as the stabilisation of the nanoscale helical structure of the twist-bend phase. In particular we focus into the mechanism of the reduction of the bend elastic constant determined by negative flexoelectric corrections and discuss why the splay elastic constant is not reduced at all. A molecular theory of elasticity of bent-core nematics, which also enables one to describe the reduction of the bend elastic constant, is considered in detail as well. Finally we consider two different tensor orientational order parameters of the twist-bend phase which describe all kinds of uniaxial and local biaxial ordering of bent-core molecules in the twist-bend phase.

Distinctive features of pretransitional behaviour between nematic phases as revealed by DDM

ABSTRACT Pretransitional behaviour, with strong softening of the bend or splay elastic constants, is characteristic of two of the nematic to nematic phase transitions reported in the last decade. Such softening is strongly reflected in the pretransitional behaviour of the thermally excited director fluctuations. Here we give a comprehensive overview of the cross-Differential Dynamic Microscopy (c-DDM) method and its application to the investigation of thermal director fluctuations and phase transitions. For this, we build on the potentialities of the method for the investigation of the standard nematic phase of E7 to compare with the pretransitional behaviour of the nematic to twist bend nematic phase transition as well as the nematic to ferroelectric nematic transition.

Novel properties of high-performance multi-component mixture for Vertically Aligned mode LCDs

ABSTRACT Vertically Aligned mode Liquid Crystal Displays (VALCDs) which have generated huge research interest due to their excellent contrast and wide viewing angle require materials with negative dielectric anisotropy. This work highlights the systematic development of a fifteen-component mixture from pure liquid crystalline compounds comprising laterally fluorinated bi-, tri- phenyl, tolane, bicyclohexane compounds and non-mesogenic compounds exhibiting negative dielectric anisotropy. The temperature dependence of birefringence (Δn), dielectric anisotropy (Δε), threshold voltage (Vth), bend elastic constant (K33), relaxation time (τ0) and rotational viscosity (γ1) as a function of temperature of this fifteen-component nematic mixture have been reported. This mixture exhibits a high Figure of Merit (FoM) which is desirable for reducing the device response time. Additionally, the orientational order parameter (OOP) values, activation energy (Ea), visco-elastic co-efficient (γ1/K33) and material parameters (A 0 ) have also been reported. The effect of pretilt angle in the alignment layers on the threshold voltage (Vth) and switching time (τ0) to ascertain the applicability of this material in Vertically Aligned mode Liquid Crystal Displays (VALCDs) have also been discussed.

Optical and flexoelectric biosensing based on a hybrid-aligned liquid crystal of anomalously small bend elastic constant

Liquid crystal (LC)-based biosensors rely on the response of the LC molecules to perturbation generated by analytes at the interface, leading to the susceptible change in molecular alignment or orientation. The sensitivity of these biosensors is primarily dependent on the LC's material properties and surface anchoring strength. By incorporation of an unconventional mesogenic compound (CB7CB) coupled with the hybrid-alignment cell configuration, this work presents a binary nematic LC for label-free biosensing, manifesting a novel sensing technology that takes advantage of CB7CB-induced flexoelectricity in the transducer. Herein, we prepared LC mixtures by blending a typical rod-like nematic LC (E7) with the bent-core mesogen CB7CB in various weight ratios and studied the effect of the CB7CB content on E7/CB7CB-based biosensing performance in vertically aligned and hybrid-aligned nematic (HAN) cells. Owing to the anomalously small bend elastic constant K33 in CB7CB, the mixture designated CB45 with the highest CB7CB weight percentage (45 wt% in this study) was best applicable to biosensing in HAN cells. When observed under a polarizing optical microscope, CB45 in the HAN geometry showed the capability of detection of as low as 10−10 g/mL for the protein standard bovine serum albumin (BSA). Moreover, the quantitation of the assay was fulfilled by both dielectric and light transmission measurements of the hybrid-aligned cholesteric CB45/R5011. The limit of detection of 7 × 10−10 g/mL was achieved by spectrometric analysis. To the best of our knowledge, this work is the first to demonstrate flexoelectric biosensing on the basis of flexoelectric polarization associated with giant flexoelectricity in CB7CB partially constituting the LC transducer.

Semiflexible polymer solutions. II. Fluctuations and Frank elastic constants.

We study the collective elastic behavior of semiflexible polymer solutions in a nematic liquid-crystalline state using polymer field theory. Our polymer field-theoretic model of semiflexible polymer solutions is extended to include second-order fluctuation corrections to the free energy, permitting the evaluation of the Frank elastic constants based on orientational order fluctuations in the nematic state. Our exact treatment of wormlike chain statistics permits the evaluation of behavior from the nematic state, thus accurately capturing the impact of single-chain behavior on collective elastic response. Results for the Frank elastic constants are presented as a function of aligning field strength and chain length, and we explore the impact of conformation fluctuations and hairpin defects on the twist, splay, and bend moduli. Our results indicate that the twist elastic constant Ktwist is smaller than both bend and splay constants (Kbend and Ksplay, respectively) for the entire range of polymer rigidity. Splay and bend elastic constants exhibit regimes of dominance over the range of chain stiffness, where Ksplay > Kbend for flexible polymers (large-N limit) while the opposite is true for rigid polymers. Theoretical analysis also suggests the splay modulus tracks exactly to that of the end-to-end distance in the transverse direction for semiflexible polymers at intermediate to large-N. These results provide insight into the role of conformation fluctuations and hairpin defects on the collective response of polymer solutions.

Fast-relaxation, dye-doped cholesteric liquid-crystal smart window with a perfect planar state

A fast-relaxation dye-doped cholesteric liquid crystal (DDCLC) smart window without any defects is prepared by the doping of a low bend elastic constants liquid crystal dimer 1″,7″-bis-(4-cyanobiphenyl-4′-yl)heptane (CB7CB). The ratio of the bend elastic constant to the twist elastic constant of the liquid crystals (LCs) is adjusted so that it equates to unity. The transient planar (TP) state and the planar (P) state are combined, so the relaxation time from the homeotropic (H) state to the P state is greatly. Moreover, the oily streaks of the P state are removed and the light scattering is lessened. The polarisation-independent DDCLC smart window switches between three states: the haze-free dark state, the high-haze dark state and the transparent state. The smart window can be used in situations where absorbed sunlight reduces room temperature and protects privacy.

In situ measurements of twist and bend elastic constants in the oblique helicoidal cholesteric.

Unique electro-optical properties of the oblique helicoidal cholesteric (Ch_{OH}) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the Ch_{OH} period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of Ch_{OH} to the electric field to measure the elastic constants of twist K_{22} and bend K_{33} directly in the cholesteric phase. The temperature dependencies of K_{22} and K_{33} allow us to determine the range of the electric tunability of the Ch_{OH} pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of Ch_{OH}-based optical devices.

Elastic and electro-optical properties of flexible fluorinated dimers with negative dielectric anisotropy

ABSTRACT We report the synthesis and the temperature dependencies of optical, dielectric, and elastic properties of four homologous dimeric mesogens in the uniaxial nematic (N) phase. The studied dimers are derived from 2ʹ,3ʹ-difluoroterphenyl units connected via flexible alkyl chains. The compounds differ in the length of either the flexible alkyl chain or the terminal groups. These achiral bimesogens exhibit the twist-bend nematic (NTB) phase with a nanoscale pitch of the modulated nematic director, as established by the freeze-fracture transmission electron microscopy. All four homologs have negative dielectric anisotropy owing to the permanent dipole oriented normal to the long molecular axes. A longer flexible bridge length yields an expanded temperature range of the N phase, stronger dielectric anisotropy, larger birefringence and bend elastic constant . Longer alkyl terminal chains increase birefringence but decrease the absolute value of dielectric anisotropy and . All four bimesogens show a dramatic decrease of down to ~0.5 pN on approaching the N-NTB transition. A longer bridge yields a longer period of twist-bend modulation in the NTB phase.

Anchoring-induced nonmonotonic velocity versus temperature dependence of motile bacteria in a lyotropic nematic liquid crystal.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

Combined electric and photocontrol of selective light reflection at an oblique helicoidal cholesteric liquid crystal doped with azoxybenzene derivative.

An oblique helicoidal cholesteric liquid crystal Ch_{OH} represents a unique optical material with a single-harmonic periodic modulation of the refractive index and a pitch that can be tuned by an electric or magnetic field in a broad range from submicrometers to micrometers. In this work, we demonstrate that the oblique helicoidal cholesteric doped with azoxybenzene molecules can be tuned by both the electric field and light irradiation. The tuning mechanism is explained by the kinetics of trans-cis photoisomerization of the azoxybenzene molecules. At a fixed voltage, UV irradiation causes a redshift of the reflection peak by more than 200 nm. The effect is caused by an increase of the bend elastic constant of Ch_{OH} under irradiation. The demonstrated principle has the potential for applications such as smart windows, sensors, tunable lasers, and filters.

Photo-driven effects in twist-bend nematic phases: Dynamic and memory response of liquid crystalline dimers

We apply UV light to control the stability of twist-bend nematic phases, NTB, and conventional nematic phases, N, in three new liquid crystalline nonsymmetric dimers containing cyanobiphenyl and light-responsive azobenzene fragments connected by a hexyloxy spacer. The dynamic and static (5 kHz) dielectric responses of (E)-4′-(6-(4-((4-(ethoxy)phenyl)diazenyl)phenoxy)hexyl)-[1,1′-biphenyl]-4-carbonitrile, CB6OAzO2, (E)-4′-(6-(4-((4-(hexyloxy)phenyl)diazenyl)phenoxy)hexyl)-[1,1′-biphenyl]-4-carbonitrile, CB6OAzO6, and (E)-4′-(6-(4-((4-hexylphenyl)diazenyl)phenoxy)hexyl)-[1,1′-biphenyl]-4-carbonitrile, CB6OAz6, are measured at different temperatures, in planar and homeotropic alignments, by the application of bias and alternating electrical fields. The three CB6OAz(O)n dimers show high values of the dielectric mean, ε¯, and dielectric anisotropy, Δε, due to the dipole moment associated with the cyanobiphenyl groups. The absence of the ether linkage to the terminal chain in CB6OAz6 reduces the NTB - N transition temperature and increases the bend elastic constant, K3, compared to those seen for CB6OAzO6. Isothermal phase transitions are promoted by light-irradiation, via trans-to-cis photoisomerisation of the azobenzene units, resulting in the disruption of the liquid crystal order and appearance of re-entrant nematic and isotropic phases at low temperatures. It is possible to control the dynamics and reversibility of these transitions by varying the chemical structure of the new dimers, the temperature and UV light dosage. This may be exploited in devices using multiple external stimuli.

On the measurement of the bend elastic constant in nematic liquid crystals close to the nematic-to-SmA and the nematic-to-NTB phase transitions

ABSTRACT We propose to measure the ratio of the bend elastic constant over the splay elastic constant of a nematic phase by using an optical method based on the measurement of the birefringence of homeotropic/planar hybrid samples. This method is compared to the classical measurements using the Freedericksz transition under AC electric field and its advantages and disadvantages are discussed. Both methods are applied to the measurement of and close to the nematic-to-SmA phase transition of the liquid crystal 8CB and the nematic-to-NTB phase transition of the mixture 8CB + 50 wt% CB7CB. The role of flexoelectricity in these measurements is analysed, as well as the role of the pretilt angle and the anchoring energy of the molecules on the plates limiting the samples.

Dielectric and viscoelastic investigations in a binary system of soft- and rigid-bent mesogens exhibiting the twist-bend nematic phase

We describe the dielectric and viscoelastic behaviour of a binary system consisting of rigid core and soft-bent nematogens, with the latter exhibiting in addition to the conventional nematic (N), the twist-bend nematic (NTB) phase. The propensity of bent architecture towards the twist-bend structures is evident from the fact that NTB phase gets induced by the addition of even a small amount of the soft-bent material, and exists over a large range of concentration. The salient features of the study include stronger antiparallel coupling, trend reversal in the thermal variation of the permittivity and its average value, observation of two relaxation processes corresponding to the director and cluster modes, significantly concentration-dependent splay and bend elastic constants along with drastic lowering of the elastic anisotropy. Thermal variation of rotational viscosity associated with the Freedericksz transformation for the different mixtures are also presented. These observations are explained using conformational changes of the individual molecules and cluster formations unique to bent structures exhibiting liquid crystallinity.

Extremely small twist elastic constants in lyotropic nematic liquid crystals

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

Influence of planar anchoring on escaped-twisted configurations of liquid crystals in a cylindrical cavity

ABSTRACT Lyotropic chromonic liquid crystals (LCLCs) confined in cylindrical cavity can form an escaped-twisted (ET) configuration, resulting from the saddle-splay elastic constant is great much than twist elastic constant. The thermotropic liquid crystal 5CB does not meet the conditions for the formation of ET configuration, but it can be achieved under the appropriate planar anchoring and the action of chiral dopant. The equilibrium configuration of nematic liquid crystals confined in cylindrical cavities with azimuthal and axial surface anchoring conditions respectively is studied by the elastic continuum theory and the difference iterative method. We obtain the analytical solution of the distribution of the director without chiral dopant and the numerical solution of the chiral dopant. We find that the planar anchoring, the saddle-splay elastic constant and the chirality determine whether an ET configuration is formed. Furthermore, the cavity radius and the bend elastic constant can affect the value of twist angle. It provides a good theoretical basis for the determination of anchoring energy and saddle-splay elastic constant.

A Landau-de Gennes theory for twist-bend and splay-bend nematic phases of colloidal suspensions of bent rods.

We develop a phenomenological Landau-de Gennes (LdG) theory for lyotropic colloidal suspensions of bent rods using a Q-tensor expansion of the chemical-potential dependent grand potential. In addition, we introduce a bend flexoelectric term, coupling the polarization and the divergence of the Q-tensor, to study the stability of uniaxial (N), twist-bend (NTB), and splay-bend (NSB) nematic phases of colloidal bent rods. We first show that a mapping can be found between the LdG theory and the Oseen-Frank theory. By breaking the degeneracy between the splay and bend elastic constants, we find that the LdG theory predicts either an N-NTB-NSB or an N-NSB-NTB phase sequence upon increasing the particle concentration. Finally, we employ our theory to study the first-order N-NTB phase transition, for which we find that K33 as well as its renormalized version K33 eff remain positive at the transition, whereas K33 eff vanishes at the nematic spinodal. We connect these findings to recent simulation results.

Accurate determination on the pre-tilt angle of liquid crystal cell by combining optical and electrical measurement

ABSTRACT In order to accurately determine the pre-tilt angle, we proposed a systematic method by combining optical and electrical measurement. First, the pre-tilt angles of the parallel and vertical aligned nematic liquid crystal (LC) cell with a large thickness (>10 μm) were measured by the crystal rotation method. Then, the material parameters of E7, including the dielectric constant and the splay and bend elastic constant, were obtained by using the dual-cell capacitance model and comparing the capacitance-voltage (C-U) curves of the thick cells. Finally, the pre-tilt angles of two thin LC cells to be tested were determined by theoretical and experimental fitting of their normalised C-U curve, which are 1.80°±0.04° and 3.50°±0.02°, respectively. Our method not only has relatively high accuracy, but also is not limited by the thickness and mode of LC cell.