Freedericksz Transition Research Articles

MODELING OF THE DYNAMICS OF A LIQUID CRYSTAL UNDER THE ACTION OF WEAK PERTURBATIONS

We study dynamic processes in liquid crystals using a simplified mathematical model in which a liquid crystal is considered as a finely dispersed continuous medium with rotating particles that has elastic resistance to volume deformation and viscoelastic resistance to the relative rotation of particles. The oscillatory regime of rotational motion described by the Klein–Gordon equation for tangential stress is studied. Moment interactions of particles due to the inhomogeneity of the rotation field are taken into account. The dispersion properties described by a subsystem of two equations for tangential stress and angular velocity are investigated. These equations are used to numerically analyze the rotation field in a liquid crystal under the action of tangential stress caused by the thermal expansion of a metal plate at the boundary. We consider the problem of perturbation of an extended layer of a 5CB liquid crystal by an electric field generated by charges on capacitor plates located periodically along the layer. Singularities of the electric potential at the ends of the capacitor plates are selected explicitly. Some results of computations simulating the Freedericksz effect in the liquid crystal layer are presented.

Effect of fullerenes C60 on dielectric relaxation, electric conductivity, and electro-optic properties of 4-cyano-4′-pentylbiphenyl

Effect of fullerenes C60 on dielectric relaxation, electric conductivity, and electro-optic properties of nematic liquid crystal 4-cyano-4′-pentylbiphenyl is investigated. It is shown that the inclusion of fullerenes into liquid crystal leads to decreasing of the clearing temperature and the order parameter. In this case, the transverse component of the real part of dielectric permittivity increases while the longitudinal component decreases. A maximum of dielectric absorption shifts to the low-frequency region. The capture of moving ions by fullerenes leads to a decrease of electric conductivity. The elastic constant, rotational viscosity and switching times decrease while the threshold voltage of Freedericksz effect increases.

Freedericksz Transitions in Twisted Ferronematics Subjected to Magnetic and Laser Field

The influence of the anchoring forces on the Freedericksz transition in twisted ferronematics simultaneously subjected to magnetic and laser fields is studied in this work. Using the elastic continuum theory and Gouchen model for molecular anchoring on the cell support plates, the critical field and the saturation field were calculated as a function of the laser intensity and anchoring strength for two types of ferronematics based on 5CB and CCN-37 liquid crystals.

Dielectric relaxation, electric conductivity, and electro-optic properties of SWCNT-doped liquid crystal 5CB

The effect of single-walled carbon nanotubes (SWCNTs) on the dielectric, conductivity, and electro-optic properties of nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) has been studied. It was shown that the additive of SWCNTs with concentration of 0.5% leads to an increase in the order parameter of 5CB. In this case, the clearing point is raised, the longitudinal component of the dielectric permittivity increases while the transverse component decreases. The incipient percolation effect promotes to the dominance of hopping electron conductivity over ionic conductivity, leading to an increase in specific conductivity. The elastic splay constant of 5CB is enhanced and, accordingly, the threshold voltage of the Freedericksz effect increases in this situation. An increase in distance between LC molecules leads to decreasing of viscosity. As a result, the flip-flop motion of molecules become easier and the switching times are also reduced.

Electro-optical performance of nematic liquid crystals doped with gold nanoparticles

The effect of gold nanoparticles on the dielectric, electro-optical, and rheological properties of the ZhK-1289 liquid-crystal mixture that define the response time of liquid-crystal devices with a concentration range of 0.06–5 wt% was investigated in this study. A phase diagram of the obtained composites was formed demonstrating an increase in the clearing temperature and a broadening of the mesophase existence range in the case of doping nanoparticles. It was found that in the obtained dispersions there are structural rearrangements in the low concentration range leading to an increase in the lateral bending stiffness of the liquid-crystal matrix, a decrease in the response time and threshold voltage of the Freedericksz transition, and also an increase in the anisotropy of the dielectric permittivity and the refraction index. The improvement of the electro-optical performance of the liquid crystal can be caused by the nanoparticle adsorption of impurity ions, which reduces the field-screening effect in the liquid crystal. According to the results obtained in this study, the optimal values of the physical parameters of liquid-crystal composites doped with gold nanoparticles for their application in practice are achieved in a concentration range of 0.5–1 wt%.

Polarization grating based on liquid crystals doped with ferroelectric nanoparticles

ABSTRACT We present a theoretical model in the framework of elastic continuum theory to describe the behaviour of a liquid crystalline host doped with ferroelectric nanoparticles acting as a liquid crystal polarization grating device. The effect of ferroelectric impurity dopants in liquid crystals and the Freedericksz transition is studied. We obtain the critical thickness and voltages of the system and find that, as in the case of pure liquid crystal devices, the critical voltages for weak anchoring conditions would be lower than those in a strong anchoring case. We also investigate the dynamic behaviour of the system and obtain the switching on and off times for the nano-doped cells with strong and weak anchoring conditions on the surfaces. The effects of the flow are excluded in our calculations. The findings show that the rise time of the suspension is lower than that of the pure liquid crystal, and switching times will be prolonged when the anchoring strength is reduced. Our results are consistent with existing experimental reports and may be useful for many applications in the industry. Obviously, electrically control is definitely fundamental in the operation of many liquid crystal devices such as displays, beam steering devices, and liquid crystal modulators.

Freedericksz transition in a dual-frequency nematic liquid crystal

The Freedericksz transition was investigated in a dual-frequency liquid crystal consisting of a mixture of 2-chloro-4-(4-pentylbenzoyloxy)benzoate and N-(4-methoxybenzylidene)-4-butylaniline, in which dielectric anisotropy strongly depends on the frequency of the applied ac electric field. Because the threshold voltage for the transition from an undistorted state of orientation to a distorted one is a function of the dielectric anisotropy and of the Frank elastic constants, the threshold voltage was expected to depend on the frequency. The threshold voltage increased steeply as the frequency approached the crossover frequency at which the dielectric anisotropy vanished and the threshold voltage eventually diverged. Furthermore, we examined the Freedericksz transition under ac voltages of two different frequencies.

Pseudopolar smectic- C phases of azo-substituted achiral bent-core hockey-stick-shaped molecules

We report experimental studies on an azo-substituted compound consisting of bent-core hockey-stick-shaped molecules. The experimental results establish two pseudopolar tilted smectic phases, which are characterized by an in-plane axial-vector order parameter in addition to tilt order in the smectic layers. Electro-optical measurements in the mesophases indicate that the birefringence of the sample strongly depends on the applied electric field. We develop a theoretical model to account for this observation. The change in the birefringence of the sample arises from the field-induced reorientation of the tilt plane of the molecules in the layer above a threshold field. The effect is analogous to the field-induced Freedericksz transition which is quadratic in the applied electric field.

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals.

We apply the minimum-energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle-point structures. When the applied voltage exceeds its critical value below the threshold of the Fréedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle-point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths.

Photoswitchable Bent-Core Nematic Liquid Crystals with Methylated Azobenzene Wing Exhibiting Optic-Field-Enhanced Fréedericksz Transition Effect

We have investigated two new series of unsymmetrical four-ring bent-core molecules with methylated azobenzene wings exhibiting nematic mesophase. The difference between the two series was in the relative position of the methyl (−CH3) substituent with respect to the azo (−N═N−) linkage in the molecule. Single-crystal X-ray diffraction analysis unravels significant insights into the spatial molecular arrangement and molecular stacking interactions of these bent-core systems. The materials were able to show photoswitching behavior and photomasking effect in the liquid-crystalline state via nematic to isotropic (order to disorder) transition when illuminated with UV light. In solid state, the materials exhibit photochromism upon UV light exposure. One of the representative compounds (2/12) was studied to observe the optically enhanced Freedericksz transition (FT) effect stimulated by UV light intensity. A prototype of phase grating has also been devised based upon the observed FT-enhanced effect that has a pr...

Uniqueness of director configuration states for liquid crystals in the case of weak anchoring

Abstract In a thin layer of liquid crystal the configuration of the director field depends on the interaction between the elastic properties of the material, the thickness $d$ of the layer, the boundary conditions and the external fields that may have been applied. Suitable combinations of these factors can give rise to distorted configurations (Freedericksz transitions). In this paper we assume the Oseen-Frank model for the energy and that the director field depends only on the direction orthogonal to the layer; we assume also weak anchoring conditions at the two bounding surfaces, and we mainly study the problem of uniqueness of such distorted configurations. More precisely, we first consider the nematic case in the presence of a magnetic field $\mathbf H$, and we prove the uniqueness of the stable configuration provided the magnitude of $\mathbf H$ is between two critical thresholds, simplifying some results already known in the literature, and calculating explicitly the critical thresholds. Then we study the case of a cholesteric liquid crystal without external field. In this case the director field tends to form a right-angle helicoid around a twist axis orthogonal to the layer, and we have distorted configurations (namely oblique helicoid) for suitable value of $d$. Also in this case, with suitable restrictions on the elastic constants in the Oseen-Frank energy, we find two critical thresholds for $d$, and we prove the existence of only one stable director configuration if $d$ is between them.

Electric Freedericksz transition in nematic liquid crystals with graphene quantum dot mixture

A theoretical model to explain the Freedericksz transition for a nematic liquid crystal with graphene quantum dots adding in electric field below the instability area is proposed. A mathematical formula for the critical voltage was obtained by elastic continuum theory combined with Burilov - Zakhlevnykh anchoring model, classical electrostatic principles and temperature dependence of elastic constant. We compared the results with the experimental data recorded for three LC samples and a good agreement between them was found encouraging us to propose this model as a tool for theoretical analysis of graphene quantum dot's dispersions in liquid crystals.

Holographic Formation of Non-uniform Diffraction Structures by Arbitrary Polarized Recording Beams in Liquid Crystal-photopolymer Compositions.

In this work, the theoretical model of non-uniform diffraction structures’ holographic formation in liquid crystal-photopolymer (LC-PPM) composite materials with a dye-sensitizer is developed. The model takes into account the arbitrary character of amplitude and phase spatial distributions of recording light field, its arbitrary polarization state and also a non-linearity of the recording process. Two the most common types of liquid crystal-photopolymer composite are investigated: Holographic polymer-dispersed liquid crystals (H-PDLC) and polymer-stabilized liquid crystals (PSLC). Numerical simulations for the most common cases of holographic formation schemes are made. It is shown that due to the photo-induced Freedericksz transition, in the case of arbitrary polarization states of recording light beams, the non-uniform polarization diffraction grating (PDG) is formed in LC-PPM. Numerical simulations’ results show that PDG’s contribution to the change of the dielectric tensor of the media is comparable with the contribution of the photopolymerization-diffusion process.

Reduced power consumption in nickel zinc ferrite nanoparticles doped blue phase chiral nematic liquid crystal devices

The effect of nickel zinc ferrite (NZFO (Ni0.5Zn0.5Fe2O4)) nanoparticles in reducing the threshold voltage of blue phase (BP) in chiral nematic liquid crystal (CNLC) was studied at room temperature. Due to low concentration selected for doping, the structure of CNLC and the temperature window of BP is maintained in entire LC range. The significant reduction in threshold voltage (5.5V) for Freedericksz transition is recorded for doped CNLC. Strong interaction between guest NZFO nanoparticles and host, aligns the CNLC molecule in an ordered structure to considerably enhance dielectric permittivity and anisotropy of CNLC doped with 0.05wt% NZFO nanoparticles to reduce threshold voltage. The presence of NZFO nanoparticles reduces the impurity ions and associated free energy in CNLC, which lead to the observed decrease in dielectric loss and elastic constant, respectively, to contribute towards reduction in driving power (by ~50%) of BP based displays. The improved photoluminescence intensity of CNLC, in the presence of NZFO, promises as a potential material for optoelectronic devices.

Electrically tuned whispering gallery mode microresonator based on Kagomé photonic crystal fibers infiltrated with nematic liquid crystals.

In this study, an electrically tunable whispering gallery mode (WGM) microresonator based on Kagomé hollow-core photonic crystal fiber (HC-PCF) is proposed by infiltrating the cross-sectional air holes with nematic liquid crystals (NLCs). Experimental results indicate that the LC molecules turn out in planar alignment. As the applied electric field strength gradually increases, the WGM resonance wavelengths shift toward the longer-wavelength region. The Freedericksz transition threshold of the proposed Kagomé HC-PCF microresonator is experimentally proved to be around 1.2 V μm-1. The electrically tunable microresonator, integrated with NLCs, is anticipated to find potential applications in optical filtering, all-optical switching, and electrically controlled micro-optics devices.

High-Frequency Regime of the Acoustical Freédericksz Transition in Nematic Liquid Crystals

A novel approach to the acoustical Freedericksz transition in the high-frequency regime is developed. The prominent role played by bulk viscosities is highlighted. Using experimental data, it is shown that α/α4 = 2.7 × 103, where the combination α ≡ ρ1 + ρ2 + ρ3 + α1 + α4 + α5 + α6 consists of shear and bulk viscosities of a nematic. The magnitude of this ratio is in agreement with what is found in fluids composed by molecules possessing several internal degrees of freedom.

Effect of Sm- A short-range order on the activation energies of translational and rotational viscosities of nematic liquid crystals with highly polar molecules

We report experimental studies on the temperature-dependent translational and rotational viscosities of a few nematic liquid crystals made of highly polar molecules. Cyanobiphenyl (nCB) with longitudinal and cyanobicyclohexane molecules (CCN-mn) with transverse dipole moments were chosen and the measurements were made in the nematic phase. The translational viscosity (shear viscosity) is measured by using a rheometer and the rotational viscosity is measured from the dynamics of the Freedericksz transition by measuring the optical phase-retardation decay of the sample. The associated activation energies are obtained from the fitting of the appropriate equation in the nematic phase. Only 8CB and CCN-47 exhibits N to Sm-A phase transition and their activation energies of translational and rotational viscosities are larger compared to the shortest homologs in the respective series. Both activation energies of 8CB are significantly larger than that of CCN-47. The temperature-dependent steady states of the director distribution under shear are comprehensibly reflected in the rheodielectric measurements of 8CB than that of CCN-47. The results are explained based on the differences in the Sm-A short-range orders and the critical slowing down of the order parameter fluctuations. We present a simple physical model of molecular association that gives rise to different Sm-A short-range orders in both classes of compounds.

Magnetic Freedericksz transition in a ferronematic liquid crystal doped with spindle magnetic particles

In this work we studied new composite ferronematic system based on the liquid crystal 4-n-hexyl-4′-cyanobiphenyl (6CB) doped with hematite spindle-like magnetic particles. We experimentally showed that magnetic moments of the elongated spindle particles are oriented perpendicularly to their main axes. It is a fundamental difference of our systems from ferronematics, which were synthesized before by many authors. For a research of magnetic and orientational properties of new composite materials, the ferronematic samples were prepared with different length of the particles and with the volume concentrations of solid impurity ϕ1=10−3, ϕ2=10−4 and ϕ3=10−5. The structural Freedericksz transition in ferronematic samples were observed by capacitance measurements in a capacitor made of ITO-coated glass electrodes. Experimental results showed a decrease of the critical field in the ferronematic samples in comparison with the pure 6CB, and an increase of the threshold shift with a growth of both the volume fraction of solid impurity and the length of particles. The response of capacitance to low external magnetic field - far below the magnetic Freedericksz transition threshold of prepared samples was also observed experimentally. For a theoretical description of this magnetically induced behavior of composite systems, the continual model of ferronematics with bistable coupling between colloidal particles and the nematic matrix was used. This theory permits the equilibrium tilted orientation of the particles with respect to the nematic director. We showed that it creates a so-called “pretilt angle effect” which explains the behavior of the ferronematic systems in a low field regime as well as decrease of the threshold field and the dependence of this field on the volume fraction of solid impurity and the length of the particles.

Influence of Ionic Surfactant on the Anchoring Energy of Liquid Crystal with a Surface Investigated Using Magnetic Threshold Fields of Freedericksz Transition

Influence of Ionic Surfactant on the Anchoring Energy of Liquid Crystal with a Surface Investigated Using Magnetic Threshold Fields of Freedericksz Transition

Electromagnetic coupling in nematic liquid crystals modeled as microcontinua

A continuum micromorphic approach to nematic liquid crystals is exploited in order to describe electro-magneto-elastic coupling effects. Nematic microdeformation is modeled by relating microinertia, electric dipole and quadrupole densities to microrotation. Accordingly, polarization and magnetization are obtained together with a constitutive law for magnetic induction. The coupled system of balance laws for linear and angular momentum and Maxwell’s equations is employed to model equilibrium for an homeotropic structure of a nematic layer subject to electric and magnetic fields, assuming strong anchoring on the layer’s boundaries. It is shown that the trivial solution of null deformation allows for a not uniform magnetic field in the presence of a not null applied electric potential. The magnetic field induced Freedericksz transition is derived obtaining a threshold value of magnetic field which depends on the electric potential. Numerical results show an hysteresis behavior of the deformation solution just behind the threshold field, which is compatible with a first order, magnetic induced transition.