Marek Andrzej Kojdecki

Composite Method for Determination of Liquid Crystal Material Parameters

Abstract A stable method for the determination of the nematic liquid crystal material parameters, such as the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility, the electric permittivities and either the coupling between the nematic molecules and the substrate at the planar liquid crystal cell boundary (i.e. the director field boundary value), is presented in the work. The method consists of two stages: firstly the effective electric permittivity of planar nematics cell is measured as a function of external electric and magnetic fields, secondly the coefficient inverse problem is solved numerically using the experimental data to determine the values of material parameters. The coefficient inverse problem is posed in a variational way as a problem of nonlinear mean-square fit of the calculated nematics layer characteristics to the measured ones. The description of phenomena is based on Ericksens - Leslies theory. The unknown material parameters serve in this approach as the fit parameters, the best values of which corresponding to the best possible approximation of the experimental data by the refined mathematical model are to be found. The method was successfully used for the determination of the material parameters of PCB and can be applied to every nematics.

Interference Method for Determining Dispersion of Refractive Indices of Liquid Crystals

An efficient, quick and pretty accurate interference method for determining dispersions of ordinary n o and extraordinary n e refractive indices and optical anisotropy of nematic liquid crystals, i.e., ne(λ), no(λ) and Δn(λ) ≡ n e (λ)–no(λ), as functions of wavelength λ (in visible and near infrared region), is presented. The method relies on measurements of positions of interference fringes in spectrogram produced by a flat-parallel nematic liquid crystal cell in only one run.

Optical Methods for Determining Anisotropy of Diamagnetic Susceptibility and Other Material Parameters of Nematics by Using Cells of Varying Thickness

ABSTRACT Wedge cells (of the wedge angle of the order of few milliradians) were used for studying Fréedericksz transition of splay-bend type. The phase shift between ordinary and extraordinary rays of light normally incident on the cell boundary was used as a physical quantity monitoring the state of the director field inside the cell in selected zones equivalent to flat-parallel cells of different thickness. The optical response was measured as a function of a voltage or a magnetic field (or both of them, crossed or parallel). Experiments were performed with two cells, filled with the 4′-pentyl-4-cyanobipfenyl liquid crystal (5CB), of different cover coatings providing strong or weak nematics-substrate coupling. Four different methods were applied for determining the anisotropy of diamagnetic susceptibility of the nematics after results of measurements, separately or simultaneously with the splay or bend elastic constants or the nematics-substrate coupling characteristics. The resulting values of material parameters are compared and the features of the methods are commented.

Morphology and molecular organisation of liquid-crystalline perylene-3,4,9,10-tetra-(n-hexylester) deposited on a solid substrate

Liquid-crystalline perylene-3,4,9,10-tetra-(n-hexylester) forms characteristic dendritic or flower-like structures at room temperature when it is deposited on a hydrophilic glass substrate using the zone-casting technique. It was found that such unique structures were not possible to be created simply by recrystallisation of this dye from a liquid-crystalline columnar phase. On the basis of the observations using a confocal microscope and the study of wide angle X-ray scattering (WAXS) as well as the analysis of the absorption and fluorescence spectra, some conclusions, concerning the molecular organisation in the dendritic structure, are drawn. Based on the research, one can assume that the dendrites are formed by columnar molecular aggregates with the column axes parallel to the substrate. Such an organisation of the molecules can be interesting from the point of view of organic electronics.

Method for Determining Material Constants of Nematic Liquid Crystals by Use of Wedge Cells

A wedge cell of the wedge angle of order of few milliradians was used to measure the phase shift between ordinary and extraordinary rays of transmitted light, for the Fréedericksz transition induced by a magnetic or an electric field. A nematic liquid crystal, PCB, filling the cell, was of the planar alignment enforced by the treatment of the flat boundary plates. A polyimide, MK8–poly (amic acid), was used as aligning substance. A system of interference fringes appeared in the cell placed in normally incident light between the analyser and the polariser crossed. In the neighbourhood of each fringe the cell can be considered as a flat-parallel one and hence it is equivalent to a system of flat cells of different precisely determined thickness. The dependence of the phase shift on applied external fields was measured for several interference fringes. The nematic liquid crystal material parameters (the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility and the boundary tilt angle as a function of the torque) were determined by fitting the calculated characteristics to the measured ones.

Composite Method for Measurement of Splay, Twist and Bend Nematic Elastic Constants by Use of Single Special In-Plane-Switched Cell

A method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is proposed. The main concept relies on exploiting only electric field in a plane-parallel liquid crystal cell of special configuration with thin transparent comb-like electrodes on one cover and usual transparent plane electrode on the other. Rubbing in direction parallel to comb electrode stripes enforces homogeneous planar or homeotropic orientation of nematic molecules. Fréedericksz’ transition of pure splay, twist or bend form is initialised by applying voltage between the electrodes appropriately. The method was tested with three different comb-like electrode configurations and three nematics: 4-pentyl-4′-cyanobiphenyl, 4-trans-4′-n-hexyl-cyclohexyl-isothiocyanatobenzene and Demus’ esters.

Study of Nematics-Substrate Coupling Characteristics and Nematics Material Parameters in Dependence on Cell Thickness by Using Wedge Cells of Different Cover Coatings

The dependence of characteristics of the coupling between nematics and substrates on the planar cell thickness was suggested in the literature. The aim of this study is verification of this hypothesis by exploiting well controlled experimental conditions and stable computational algorithms for finding the characteristics of the nematics-substrate coupling together with the anisotropy of diamagnetic susceptibility and the splay and bend elastic constants via solving inverse problems. Wedge cells (of the wedge angle of the order of few milliradians) were used for studying Fréedericksz transition of splay-bend type. The phase shift between ordinary and extraordinary rays of light normally incident on cell boundary was used as a physical quantity monitoring the state of the director field inside a cell in selected zones, equivalent to flat-parallel cells of different thicknesses. The optical response was measured as a function of voltage or magnetic field applied to a cell. Experiments were performed with several cells, filled with the 4′-pentyl-4-cyanobiphenyl nematic liquid crystal (5CB), of cover coatings made of different polyimides producing strong anchoring. The magnitudes of the anisotropy of diamagnetic susceptibility, the splay and bend elastic constants and the anchoring angle were found through fitting simulated cell optical transmittance characteristics to the measured one for each equivalent cell separately. The apparent dependence of these magnitudes on cell thickness was observed when the fitting was performed to reach the minimal fit error. This effect is interpreted as misleading and corrected by considering the fitting with the same magnitudes of material constants to all measured transmittance characteristics, with a little greater fit errors. The independence of nematics constants and anchoring angle of cell thickness is finally concluded.

Determiniation of nematic liquid crystal material parameters by solving inverse problems for different planar cells

The practical application of the composite method of the determination of nematic liquid crystal material parameters (namely the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility and the boundary tilt angle) is presented. The description of phenomena is based on the Ericksen-Leslie theory of nematics. The director field value at the nematics cell boundaries is described as a function of the torque transmitted from the deformed bulk, modeling the coupling between a nematics and a substrate. The method is based on approximate solving the coefficient inverse problem. The applied procedure of the determination of material parameters may be divided into three stages. The first one was the preparation of flat-parallel nematics cells, made of the same nematics and with the same treatment of the glass plate surfaces. The second one was the measurements of the optical response of the cells influenced by an external electric field (a voltage). Such cell characteristics contain information about the unknown magnitudes of material parameters. The final stage was the determination of the magnitudes of liquid crystal material parameters as solutions of coefficient inverse problems with measured cell characteristics as input data. The method was applied to study a system nematics PCB - polyimide PI10.

Complementary interference method for determining optical parameters of liquid crystals

ABSTRACT Wedge cells of small apex angle, filled with liquid crystals, were used to determining optical characteristics as functions of temperature for three liquid crystalline mixtures recently produced and a reference nematic. The interference fringes appearing in polarised monochromatic light (of sodium yellow line) normally incident on the cell were exploited to measure the ordinary and extraordinary refractive indices in the reflection mode and birefringence in the transmission mode. The measurements were repeated using Abbes refractometer for 6CHBT as the reference to verifying the precision. Additionally the order parameter was computed from birefringence as a function of temperature. The results confirm the usefulness of the method and provide the properties of two nematic liquid crystals of small and large birefringence and one smectic liquid crystal of medium birefringence, recently produced. The experimental systems served also to investigating phase transition between the liquid crystals and the isotropic liquid at near-clearing temperature.

Determination of nematics material parameters by measurements of Fredericksz transitions in crossed electric and magnetic fields in wedge cell

Wedge cells of the wedge angle of order of few milliradians were used to measure the threshold voltages for the Freedericksz transition in electric and magnetic fields crossed. A nematic liquid crystal, PCB, filling cells was of planar orientation enforced by the treatment of the flat boundary plates, covered with poly(amic acid) PM9. A system of interference fringes appeared in each cell placed in normally incident light between analyzer and polarizer crossed. In the vicinity of each fringe a cell could be considered as a flat-parallel one and hence it was equivalent to the system of flat cells of different precisely determined thickness. Threshold voltages, parameterized by magnetic field magnitudes were interpreted as the eigenvalues of the boundary eigenvalue problem for the operator of the second derivative; the interaction between the nematics and the substrates was assumed very strong with the anchoring direction parallel to the cell boundaries. The resulting formulae were used to determine the anisotropy of diamagnetic susceptibility and the splay elastic constant of PCB after the threshold magnitudes measured. The estimates of material parameters agreed well with those determined by the composite method.