Dynamics of jumpwise temperature pitch variations in planar cholesteric layers for a finite strength of surface anchoring

The dynamics of pitch jumps in cholesteric layers with a finite surface anchoring strength under variations in temperature is investigated theoretically. General expressions are presented that connect the dynamics of pitch jumps with the parameters that determine the process, such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter S _d = K₂₂/Wd, where W is the depth of the anchoring potential, K₂₂ is the twist elastic modulus, and d is the layer thickness. It is found that the shape of the anchoring potential significantly influences the temporal behavior of the cholesteric helix in the process of a pitch jump. To illustrate this revealed dependence of the pitch jump dynamics on the shape and strength of the anchoring potential, the problem was investigated for two different models of the surface anchoring potential for a jump mechanism in connection with the director at the surface slipping over the barrier of the anchoring potential. Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will make it possible to distinguish different shapes of the finite strength anchoring potential and, in particular, it will provide a means for determining whether the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with a finite surface anchoring strength. The optimal conditions for experimental observation of these phenomena are briefly considered.     

Surface anchoring and pitch variation in thin smectic C* layers in an electric field

The variations of the pitch of smectics C* in thin planar layers in an external electric field and their dependence on the surface anchoring are investigated theoretically. The proposed mechanism of the change in the number of half-turns of the helical structure in a finite-thickness layer upon a change in the applied field is the slip of the director on the surface of the layer through the potential barrier of surface anchoring. The equations describing the pitch variation in an external field and, in particular, the hysteresis in the jumpwise variations of the pitch for opposite directions of field variation are given and analyzed for arbitrary values of the field. For weak fields, it is found that the pitch variation in the layer is of a universal nature and is determined by only one dimensionless parameter, S _d= K ₂₂/dW, where K ₂₂ is the Frank torsion modulus, W is the surface anchoring potential, and d is the layer thickness. The possibility of direct determination of the form of the anchoring potential from the results of corresponding measurements is considered. Numerical calculations for the deviation of the director from the direction of alignment on the layer surface and pitch variations, as well as the points of pitch jumps and hysteresis in the field, are made for the Rapini model anchoring potential for values of the parameters for which the pitch variation weakly depends on the direction of the field applied in the plane perpendicular to the spiral axis of smectics C*. The changes in the pitch variation in stronger fields are discussed, and the optimal conditions for observing the discovered effects are formulated.     

Temperature variations in the director orientation and anchoring energy at the surface of cholesteric layers

Slight changes with temperature in the director orientation at the surface of a perfect planar cholesteric liquid crystal (CLC) layer, which are precursors of a jump in the pitch of the cholesteric helix, are observed by measuring the temperature dependence of the optical transmission spectra of the layer. The observed changes in the director orientation are described in the framework of the continuum theory of CLCs, supplemented with allowance for the surface anchoring forces. In particular, the angle of deviation of the director at the surface from the alignment direction at the exact temperature of the jump in pitch is expressed in terms of the anchoring potential. The relation obtained is use to find the anchoring potential in the samples. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 37–42 (10 January 1996)     

Bistable surface anchoring and hysteresis of pitch jumps in a planar cholesteric liquid crystal

The relationship between bistable surface anchoring and the pitch jump process is examined for a planar cholesteric liquid crystal. Introducing a high-order, azimuthal surface anchoring potential into a simple model to describe a cholesteric, we derive an expression for the director twist as the natural pitch of the liquid crystal is allowed to vary. Writing the energy in terms of the surface twist, we are able to determine the twists which minimize the total energy of the system. We demonstrate how a pitch jump is related to an energy exchange from one branch of metastable states to another. We then discuss how the co-existence of energy minima and their associated solution branches may help explain the thermal hysteresis observed experimentally in cholesterics in the neighbourhood of a pitch jump. The presence of a higher-order surface energy term can expand the range of anchoring strengths in which pitch jumps are possible. We also investigate the influence of bidirectional surface anchoring on the behaviour of the total energy. Intermediate quarter-turn pitch jumps can occur, depending on the relative strength of the high-order anchoring term, and these can have a significant effect on the system hysteresis.     

On mechanisms of the helix pitch variation in a thin cholesteric layer confined between two surfaces

Two possible mechanisms of the temperature-induced variation and jump of the helix pitch in a spatially bounded planar layer of a cholesteric liquid crystal (LC) was considered within the framework of the continuum theory of elasticity. These mechanisms are related to the existence of two configuration curves of the system free energy. The states with local free energy minima on each of the configuration curves correspond to topologically equivalent configurations of the LC director distribution and are quasi-equivalent in this sense. The transitions between such quasi-equivalent states are especially important in the first mechanism of the helix pitch jump proceeding without participation of defects. The second mechanism is related to transitions between the ground states of different configuration curves corresponding to topologically nonequivalent configurations. This mechanism requires either participation of disclination lines or the formation of defects.     

Polarization and pitch dependence of cholesteric blue-phase structures

For cholesteric mixtures of two biphenyl liquid crystals, we show: (1) The BPI-BPII wavelength gap vanishes discontinously with pitch, thereby suggesting two possible BPII structures. (2) The Bragg reflections are all circularly polarized, contrary to existing theories. The temperature dependence of the BPI-BPIIA wavelength is well described by Alexander's theory.     

Surface and interface properties of thin pentacene and parylene layers

To improve Organic Thin Film Transistor (OTFT) properties we study OTFT semiconductor/dielectric interfacial properties via examination of the gate dielectric using thin Parylene C layer. Structural and morphology properties of pentacene layers deposited on parylene layer and SiO₂/Si substrate structure were compared. The surface morphology was investigated using atomic force microscopy (AFM) and scanning electron microscopy (SEM). AFM topography of pentacene layer in non-contact mode confirmed the preferable pentacene grain formation on parylene surface in dependence on layer thickness. The distribution of chemical species on the surfaces and composition depth profiles were measured by secondary ion mass spectroscopy (SIMS) and surface imaging. The depth profiles of the analyzed structures show a homogenous pentacene layer, characterized with C or C₂ ions. Relatively sharp interface between pentacene and parylene layers was estimated by characteristic increased intensity of CCl ions peak. For revealing the pentacene phases in the structures the Micro-Raman spectroscopy was utilized. Conformal coatings of parylene and pentacene layers without pinholes resulted from the deposition process as was confirmed by SIMS surface imaging. For the pentacene layers thicker than 20 nm, both thin and bulk pentacene phases were detected by Micro-Raman spectroscopy, while for the pentacene layer thickness of 5 and 10 nm the preferable thin phase was detected. The complete characterisation of pentacene layers deposited on SiO₂ and parylene surface revealed that the formation of large grains suggests 3D pentacene growth at parylene layer with small voids between grains and more than one monolayer step growth. The results will be utilized for optimization of the deposition process.      

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.Received: 9 September 2003, Published online: 5 February 2004PACS: 42.70.Df Optics: liquid crystals - 61.30.-v Structure of solids and liquids: liquid crystals - 78.20.Bh Optical properties of bulk materials and thin films: theory, models, and numerical simulation     

Light scattering in cholesteric liquid crystals with a large pitch

Optical properties of cholesteric liquid crystals with a pitch larger than the wavelength of light are considered. Normal waves of the medium and the Green function of the electromagnetic field are analyzed. A general algorithm based on the application of the Kirchhoff method is proposed for calculating the scattered light intensity in media with a one-dimensional periodic structure. The WKB vector method is used for calculating the spatial correlation function of thermal fluctuations of the director. It is found that the transformation of two fluctuation modes takes place is some regions. The angular and polarization dependences of the intensity of light scattered from fluctuations of the director are calculated. It is found, in particular, that the intensity of scattering is a nonmonotonic function of the size of the system.     

Surface morphology and local magnetic properties of electrodeposited thin iron layers

Thin iron layers with different thickness were prepared by electrodeposition on the polycrystalline substrate. The surface morphology of the layers, their structure and local magnetic properties were studied using scanning tunneling microscopy (STM), X-ray diffraction (XRD) and conversion electron Mössbauer spectroscopy (CEMS). STM studies revealed the granular structure of the surface of the electrodeposited iron layers with the roughness up to 10 nm. XRD analysis proved that these layers were highly strained. The CEMS spectra showed an in-plane magnetic anisotropy in the iron layers. Isomer shift of the electrodeposited iron was different than that of the -Fe. This difference was attributed to the internal stresses existing in the electrodeposited layers.     

Electric-field-induced unwinding of ferroelectric helix in thin smectic C* layers with soft and rigid anchoring of molecules

The unwinding of a helical structure in thin films of a ferroelectric smectic liquid crystal (LC) by an external electric field has been theoretically studied using a discrete model in which every LC layer is characterized by a two-dimensional vector ξ _i (describing the orientation of molecules) and by the polarization P _i . It is established that the unwinding of the LC helix in thin films significantly differs from the well-known behavior of thick samples. In particular, discrete intermediate states (differing by an integer or half-integer number of turns) are formed in thin films for both weak and strong anchoring of molecules to a substrate surface. The physical factor responsible for this behavior is the presence of near-surface regions with thicknesses below the helix pitch and the corresponding uncompensated polarization.     

Surface instability on thin fluid layers of a binary mixture

A long-wave model for thin layers consisting of two miscible fluids is presented. The model is a development of a simplified 2D model variant which considers the temperature and the concentration fields as linear functions on the vertical coordinate and neglect the convective terms from the corresponding equations. Now, the 2D thin film equation is coupled to complete 3D energy and mass conservations equation. We discuss the extended system in the linear approximation and in the initial nonlinear stage.     

Surface morphology and Raman spectroscopy of thin layers of antimony and bismuth chalcogenides

The phonon spectra in thin layers of bismuth telluride and solid solutions of Bi_2–xSb_xTe_3–ySe_y of different composition, belonging to three-dimensional topological insulators, have been investigated by micro-Raman spectroscopy, and the morphology of an interlayer van der Waals (0001) surface in them has been studied by semicontact atomic force microscopy at room temperature. The analysis of the Raman spectra and the intensity ratio of active and inactive longitudinal optical modes depending on the composition, morphology of the interlayer surface, and thickness of the layers enabled the estimation of the effect of topological surface states of Dirac fermions, associated with the strengthening of the electron–phonon interaction as a result of resonance Raman scattering, and the identification of the compositions, in which the contribution of topological surface states becomes dominant.     

Surface waves in thin layers of conducting media in the frequency range for the skin effect

The dispersion equation for a thin layer of a conducting medium in the frequency ranges for a pronounced skin effect is derived and analyzed. Cases of inertial, normal, and anomalous skin effects are considered. The dispersion equation and its solutions correspond to surface waves of a semi-infinite medium under conditions where the thickness of the layer greatly exceeds the skin depth. New mode spectra, which depend significantly on the thickness of the layer, are obtained in the opposite limit. Zh. Tekh. Fiz. 67, 83–85 (December 1997)     

Surface anchoring energy and the Freedericksz transitions in ferronematics

This paper analyzes the influence of anchoring conditions on the two-field-induced Freedericksz transition in ferronematics. Using the Euler-Lagrange analytical method we find a correlation between the threshold intensities of the magnetic and the laser fields, the anchoring strength, the material and device parameters. The threshold fields in our case are smaller than those obtained in the rigid anchoring limit. We show that for finite anchoring energy, the saturation transition is possible, and find the correlation between the saturation fields, the anchoring strength, the material and cell parameters. Our results can be useful in designing magneto-optical devices using ferronematics.     

Enhancement of the room temperature oxidation of silicon by very thin predeposited gold layers

The oxidation of Si(111) surfaces covered with very thin layers of gold is studied by Auger and electron energy loss spectroscopies under ultra high vacuum conditions. It is found that by exposing the Au covered surface to an oxidizing atmosphere, formation of silicon dioxide occurs at room temperature on top of the substrate and the presence of SiO₄ tetrahedra is clearly seen on electron energy loss spectra. In contrast, oxidation under the same conditions of a clean Si(111) surface leads to the formation of an oxygen monolayer and no structure corresponding to Si-O bonds in SiO₄ tetrahedra are observed. This enhancement of the oxidation is attributed to a change in the hybridization state of Si atoms in a gold environment.     

Analysis of thin layers and discontinuities

A modification of the finite difference scheme for thin dielectric layers is presented and implemented into the method of lines. The thin layers may be placed between two consecutive discretisation lines, i.e. no line is inside the layer. The analysis is based on the treatment of dielectric boundaries. So, formulas for the finite difference scheme at interfaces are given, too. The expressions are tested by determining the effective index of a slab waveguide with a very thin film-layer. A comparison with the analytical solution proves the accuracy of the derived formulas. Another test was the analysis of a Bragg-grating, here only the treatment of interfaces was checked. The modified difference scheme works very well in the TE-case whereas there remain problems for the TM-polarisation.