Microscopic vs. macroscopic origin of the Lehmann effect in cholesteric liquid crystals

In a recent letter (EPL 97, 36006 (2012)), we have shown that the Leslie thermomechanical coupling cannot alone explain the Lehmann effect (namely the rotation of cholesteric droplets when they are subjected to a temperature gradient). This result was obtained by measuring in a compensated cholesteric mixture the “Lehmann coefficient” as a function of temperature both below and at the transition to the isotropic liquid. In this article, we detail these experiments and present new ones performed with other compensated mixtures and a diluted cholesteric mixture. The new results confirm the macroscopic origin of the Lehmann effect, in contrast to the Leslie thermomechanical effect that is clearly of microscopic origin.     

Lehmann rotation of cholesteric droplets subjected to a temperature gradient: Role of the concentration of chiral molecules

We present a systematic study of the Lehmann rotation of cholesteric droplets subjected to a temperature gradient when the concentration of chiral molecules is changed. The liquid crystal chosen is an eutectic mixture of 8CB and 8OCB doped with a small amount of the chiral molecule R811. The angular velocity of the droplets strongly depend on their size and on the concentration of chiral molecules. The Lehmann coefficient is estimated by using three different methods. Our results are consistent with a Lehmann coefficient proportional to the concentration of chiral molecules. We additionally show the existence of a critical size of the droplets below which they change texture and stop rotating.     

Does the electric Lehmann effect exist in cholesteric liquid crystals?

Experiments have shown that cholesteric droplets or cholesteric fingers may be put into motion by the action of an electric field. The former rotate whereas the latter drift perpendicularly to their axes. In all cases, the texture moves without visible material transport. The electric Lehmann effect was initially used to interpret these observations but, recently, alternative explanations were found, based on electrohydrodynamics. Another experiment in this area was that of Padmini and Madhusudana (Liq. Cryst. 14, 497 (1993)). Performed in 1993 with a compensated cholesteric liquid crystal under fixed planar boundary conditions, it was also explained in terms of electric Lehmann effect. We conducted the same experiment and extended it to a π -twisted planar geometry. Although our experimental results agree with those of Padmini and Madhusudana, we demonstrate that they are incompatible with an electric Lehmann effect. By contrast, an explanation based on flexoelectricity allows us to interpret the whole data set obtained in both geometries. The consequence is that there is at the moment no clear experimental evidence of the electric Lehmann effect.     

Molecular dynamics simulation of thermomechanical coupling in cholesteric liquid crystals

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross-couplings between thermodynamic forces and fluxes that are polar vectors and pseudo vectors respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque which rotates the director. This phenomenon is known as the Lehmann effect. The converse is also possible: one can drive a heat current by rotating the director. In this work a recently developed non-equilibrium molecular dynamics simulation algorithm is applied to calculate the cross-coupling coefficient between the temperature gradient and the torque for a molecular model system based on the Gay-Berne fluid. According to the Onsager reciprocity relations this cross-coupling coefficient is equal to the coupling between the director angular velocity and the heat current. The cross-coupling coefficients are found to be very small but non-zero and the Onsager reciprocity relations are satisfied within the statistical uncertainty.     

Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoids of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adjacent ellipsoids is 7.5°, so the molecules are twisted. At high densities they form a cholesteric phase where their twist axes are oriented around the cholesteric axis and the symmetry axes of the ellipsoids are approximately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a temperature gradient parallel to the cholesteric axis induces a torque that rotates the director. The converse is also possible: rotation of the director can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the torque, and the cross-coupling coefficient between the director angular velocity and the heat current have been calculated by non-equilibrium molecular dynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relations from equilibrium simulations. Two ensembles have been utilized: the ordinary canonical ensemble and another ensemble where the director angular velocity is constrained to be a constant of motion. All the methods give consistent results for the twist viscosity and the thermal conductivity. The NEMD estimates of the cross-coupling coefficients agree within a relative error of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relative error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.     

Lehmann effect in a compensated cholesteric liquid crystal: Experimental evidence with fixed and gliding boundary conditions

In a recent letter (Europhys. Lett. 80, 26001 (2007)), we have shown that a compensated cholesteric liquid crystal (in which the macroscopic helix completely unwinds) may be subjected to a thermomechanical torque (the so-called Lehmann effect), in agreement with previous findings of éber and Jánossy (Mol. Cryst. Liq. Cryst. Lett. 72, 233 (1982)). These results prove that one must take into account the chirality of the molecules and the absence of inversion symmetry at the macroscopic scale when deriving the constitutive equations of the phase at the compensation temperature. In this paper, we present the details of our experimental work and a new experiment performed in a sample treated for planar gliding anchoring. The latter experiment, coupled with a numerical simulation, supports the existence of a thermomechanical coupling in a compensated cholesteric.     

螺状相液晶旋光特性理论模拟与实验研究

利用旋光理论模拟了一种用于螺状相液晶显示器(CH-LCD)的螺状相液晶的旋光率与入射波长、螺距的关系,并从理论上给予定量分析;用磁光调制倍频法测试了这种螺状相液晶旋光率随温度变化的规律,并利用所测的旋光率的值计算得出这种螺状相液晶的螺距、折射率、及双折射率随温度变化的规律;对模拟结果给予了实验验证。     

Zigzag instability of a χ disclination line in a cholesteric liquid crystal

We studied the formation of χ disclination lines in planar cholesteric samples placed in a temperature gradient near the cholesteric to smectic A phase transition. We observed that the first simple line which forms close to the smectic-cholesteric front zigzags when it is perpendicular to the direction of planar anchoring and is straight for other orientations. This instability is similar to Herring instability for crystalline surfaces. We show numerically that it originates from a strong increase of the elastic anisotropy close to the transition. In addition, we propose a new method to measure the pitch divergence at the smectic to cholesteric phase transition.     

Defect mode emission of a dye doped cholesteric polymer network

We have observed enhanced fluorescence and laser emission due to a photonic defect mode in a dye doped cholesteric polymer network. The defect is caused by a phase jump of the cholesteric helix at the interface of two stacked layers of a cholesteric polymer film. Fluorescence spectra show an additional resonant mode inside the photonic stop band. Pulsed excitation gives rise to laser emission of the defect mode, with an exceptionally low lasing threshold. The defect mode emission has a circular polarization whose sense of rotation is opposite to that of the cholesteric helix.     

Cholesteric liquid crystals with tunable defect inside as polarization azimuth rotation amplifiers and polarization azimuth stabilizers

In the present paper, we investigate the polarization properties of the cholesteric liquid crystals (CLCs) with an isotropic/anisotropic defect inside them, and possibilities of amplification of the polarization plane rotation and stabilization of the light polarization azimuth by these systems are investigated.     

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

The new matrix and the polarization state of the transmitted light through the cholesteric liquid crystal

The cholesteric liquid crystal can be regarded as a multilayer that consists of many layer uniaxial thin films that exhibit optical rotation. For the convenient discussion of the polarization states of the transmitted wave through a cholesteric liquid crystal, a new 2×2 matrix is given, in which the matrix element is changed into the complex exponential. Here we discuss the treatment process of this method in detail and its role in the investigation of the polarization states. Using this method we easily study the polarization states of the transmitted wave. The calculated results show that the polarization states of wave will be changed when it propagates along the cholesteric liquid crystal.     

Reflection and transmission of light by cholesteric liquid crystal-glass-cholesteric liquid crystal and cholesteric liquid crystal(1)-cholesteric crystal(2) systems

Reflection and transmission of light by cholesteric liquid crystal-glass-cholesteric liquid crystal and cholesteric liquid crystal(1)-cholesteric liquid crystal(2) systems were studied. The classical Ambartsumyan method of adding layers and the concept of a sewing function were used. This approach was developed earlier in astrophysics for the theory of radiation transfer. Here, we used a version of this method adapted to wave optics. The Jones matrices are constructed for these systems. The features of the reflection and transmission spectra, optical rotation and ellipticity of polarization were studied for these systems. It is proposed to use these systems as tunable narrow-band filters and mirrors. These systems can be used, for example, to develop a variety of optical elements for lasers and of polarimetric elements in ellipsometry. The specific features of eigenpolarization are also discussed. It is shown that optical rotation of the two layers of cholesteric liquid crystals, which differ from each other only by the sign of the helix, is nonzero, and it becomes substantial in the diffraction reflection region. A unique property of these systems is the degeneracy (coincidence) of eigenpolarizations.     

From selective to wide-band light reflection: a simple thermal diffusion in a glassy cholesteric liquid crystal

Due to their helicoidal structure, cholesteric liquid crystals exhibit remarkable optical properties. Selective light reflection occurs when the pitch (repeat distance) is of the order of the wavelength of incident light propagating along the helix axis. The wavelength bandwidth, due to the optical anisotropy, is typically limited to 50 nm which is insufficient for some applications (full-colors displays, for example). By introducing a pitch gradient in the helix during a novel two-step process in a cholesteric glass, we show that reflection may occur over a wavelength bandwidth greater than 300 nm. First, the reflection bandwidth is adjusted by thermal annealing. Then, the optical properties are permanently stored by quenching the viscous material to a glass at room temperature. The two steps, pitch gradient establishment and film hardening, are independently controlled. The present process exhibits some reversibility and properties intrinsic to the glassy state are gained: laser-writing high resolution full-color images on solid films for image recording or high-density optical data-storage are indeed conceivable. Received 17 December 1998     

基于矩阵理论的螺旋液晶透射光偏振态研究

将螺旋型液品看作是N层双折射材料晶片叠合而成,而每层光轴相对于相邻的晶片有一个小的旋转.本文基于矩阵理论,研究了光在螺旋液晶中传输时偏振态的变化.经过详细的数学推导,理论研究表明.线性偏振光经过螺旋液晶后偏振态会发生改变.当满足一定的条件时,线偏振光的偏振方向旋转90°,左旋圆偏振光经过左旋螺旋液晶后转变为右旋圆偏振光.     

复指数矩阵法研究螺旋液晶光学传播特性

提出一种研究螺旋液晶光学特性的数学处理方法.螺旋型液晶可当作N层双折射材料晶片叠合而成,而相邻晶片的光轴依次旋转一个小角度.在光学转换矩阵中引入复数来研究螺旋型液晶光学性能,给出了相关的数学处理方法.研究了线性偏振光在螺旋液晶中的传播特性,并给出了光经过螺旋液晶后电场强度的矩阵表达式.研究发现,如果入射光波长等于螺旋液晶螺距,线偏振光经过右螺旋液晶后是左旋圆偏振光.理论上分析了螺旋液晶对可见光选择性反射机理.     

Determination of the liquid crystals phase transition temperatures using optical rotation effect

Using optical rotation effect, a sensitive, simple optical analytical system is developed for determining the phase transition temperatures of liquid crystals (LCs). When a monochromatic polarized light passes through LCs sample and analyzer, the light intensity changes with temperature. Especially, during the phase transition process, the intensity varies greatly due to optical rotation effect. The variation of light intensity versus variation of temperature curve shows the phase transition temperatures of LCs clearly. The phase transition temperatures of three cholesteric liquid crystals (ChLCs) and a nematic liquid crystals (NLCs) were detected by this method, and compared with those of the differential scanning calorimetry (DSC) and polarized light microscope (PLM) methods.     

Optical anisotropy of some cholesteryl esters of fatty acids

Assuming the Neugebauer relations to be valid we have made calculations with regard to the effective polarizabilities and hence the optical anisotropy in smectic and cholesteric mesophases of five cholesteryl esters of fatty acids. The variation of optical anisotropy as a function of temperature and the change in optical anisotropy as we pass from the lowest temperature in the smectic phase to the lowest temperature of the cholesteric phase are correlated with the number of C-C bonds in the alkyl end groups of the molecules. It emerges that the end groups do not contribute significantly to the effective optical anisotropy owing to the existence of rotational isomerism.     

胆甾相液晶可见光布拉格反射实验

胆甾相液晶可见光反射行为，在某种意义上与晶体粉末样品Ｘ光衍射相似，本主要提供一个巧妙而又直观的布拉格反射实验方法，并测量胆甾相结构周期－螺距与温度的关系，进而揭示胆甾相液晶热色效应的机理。     

Temperature dependence of the intrinsic Faraday rotation of ErFeO3

The Faraday rotation of ErFeO₃ as a function of temperature was measured from ambient down to the spin reorientation region (90 to 100°K) at a wavelength of 6070 Å. The intrinsic Faraday rotation increases gradually with decreasing temperature and then drops rapidly to zero in the spin reorientation region. It is concluded that the contribution of the polarized Er³⁺ magnetic moments to the measured rotation is negligible and that the Faraday effect is due almost entirely to the magnetic moments of the Fe³⁺ ions.