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.     

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.     

Surface anchoring and temperature variations of the pitch in thin cholesteric layers

The temperature variations of the cholesteric pitch in thin planar layers of cholesterics and their dependence on the surface anchoring force are investigated theoretically. It is shown that the temperature variations of the pitch in a layer are of a universal character. This is manifested in the fact that they depend not separately on the parameters of the sample but only on one dimensionless parameter S _d =K ²²/dW, where K ₂₂ is the torsional modulus in the Frank elastic energy, W is the height of the surface-anchoring potential, and d is the thickness of the layer. The investigation is performed the parameter S _d in a range where the change per unit number of cholesteric half-turns within the thickness of the layer accompanying a change in the temperature is due to the slipping of the director on the surface of the layer through the potential barrier for surface anchoring. The critical values of the parameter S _d (which are most easily attained experimentally by varying the thickness of the layer), determining the region of applicability of the approach employed, are presented. The temperature variations of the free energy of the layer and the pitch of the cholesteric helix in the layer as well as the temperature hysteresis in the variations of the pitch with increasing and decreasing temperature are investigated for the corresponding values of S _d . Numerical calculations of the quantities mentioned above are performed using the Rapini anchoring potential.     

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.     

Transformation of cholesteric orientational structures and optical textures induced by the electric field–driven ionic modification of surface anchoring

The reorientation of a cholesteric liquid crystal with a large helical pitch induced by the electric field–driven modification of surface anchoring is investigated. In the initial state, the liquid crystal cell has a homeotropic alignment of the director. An applied dc electric field produced a twisted homeoplanar structure of the cholesteric.     

Steady low shear rate cholesteric flow normal to the helical axis

Steady cholesteric flow at low shear rate normal to the helical axis is studied analytically for shear flow and plane Poiseuille flow on the basis of Leslie’s continuum theory. For general asymmetric solutions the angle made by the director at the sample centre with the primary flow is found to profoundly affect the oscillations of the apparent viscosity with pitch for pitches of the order of the sample thickness. The velocity and orientation profiles are also found to change drastically. These considerations may be important in flow experiments on long pitch cholesterics.     

Switchable two-dimensional gratings based on field-induced layer undulations in cholesteric liquid crystals

We propose switchable two-dimensional (2D) diffractive gratings with periodic refractive-index modulation arising from layer undulations in cholesteric liquid crystals. The cholesteric cell can be switched between two states: (1) flat layers of a planar cholesteric texture and (2) a square lattice of periodic director modulation associated with layer undulations that produces 2D diffraction patterns. The intensities of the diffraction maxima can be tuned by changing the applied field. The diffractive properties can be optimized for different wavelengths by appropriately choosing cholesteric pitch, cell thickness, and surface treatment.     

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.     

Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals

We employ the fluorescent confocal polarizing microscopy to image edge dislocations in cholesteric liquid crystals. Surface anchoring at the bounding plates determines the structure and behavior of defects. Two types of plates set in-plane director orientation but differ in the type of associated anchoring potentials. Plates with strong polar anchoring and nonzero azimuthal anchoring repel the dislocations, while plates with weak polar anchoring and no azimuthal anchoring allow the dislocations to escape through the boundary. To explain the results, we propose a coarse-grained model of cholesteric anchoring.     

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.     

Theory of spherulitic domains in cholesteric liquid crystals with positive dielectric anisotropy

New localized axisymmetric nonsingular solutions minimizing the Frank functional have been found for a cholesteric layer with homeotropic anchoring. They have a continuous distribution of the director field and are characterized by a convex shape. These solutions describe the so-called spherulitic domains which have been observed in a large-pitch cholesteric near the unwinding transition.     

Flexo-electric polarization and anchoring energy for a nematic liquid crystal in a hybrid cell

Summary The flexo-electric polarization of hybrid nematic cells filled with 5 CB was measured as a function of cell thickness. To this aim the pyroelectric response of a nematic layer with small amount of light absorbing dye dissolved was detected in a nematic temperature range. From the experimental data the angle of the director deviation at the homeotropic boundary was calculated as a function of cell thickness. This dependence allows the qualitative determination of the shape of the potential well for the director deviation which is inconsistent with Rapini’s sinesquared form. The ?apparent? Rapini’s anchoring energy varies with a surface director angle (at the homeotropic boundary) from 5·10⁻³ to 3.5·10⁻² erg·cm⁻². Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Surface driven transition in a nematic liquid crystal cell

Surface driven reorientation effects in a nematic liquid crystal cell caused by light-induced changes of the anchoring parameters were studied. Theoretical consideration of one-dimensional flat distributions of the director has shown that the director can undergo threshold reorientation between hybrid, homeotropic, and planar alignments as the anchoring energy varies continuously. The threshold reorientation takes place when the reference and light-induced easy axes are perpendicular. In the one-elastic-constant approximation the light-induced transition was found to be of second order as shown by a critical increase of the director thermal fluctuations in the vicinity of the transition point. These effects were experimentally studied in the cells containing 5CB liquid crystal aligned by the photosensitive azo-containing polymer layer. Zh. éksp. Teor. Fiz. 112, 2045–2055 (December 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Nonlinearities in tilt and layer displacements of planar lipid bilayers

A novel continuum model is proposed to describe the deformations of a planar lipid bilayer suspended across a circular pore. The model is derived within a new theoretical framework for smectic A liquid crystals in which the usual director n , which defines the average orientation of the molecules, is not constrained to be normal to the layers. The free energy is defined by considering the elastic splay of the director, the bending and compression of the lipid bilayer, the cost of tilting the director with respect to the layer normal, the surface tension, and the weak anchoring of the director. Variational methods are used to derive the equilibrium equations and boundary conditions. The resulting boundary value problem is then solved numerically to compute the fully nonlinear displacement of the layers and tilt of the lipid molecules. A parametric study shows that an increase in surface tension produces a decrease in the deformation of the lipid bilayers while an opposite effect is obtained when increasing the anchoring strength.     

Surface Anchoring and Director Distribution in a Grandjean–Cano Wedge

Theoretical calculations of the director distribution in a Grandjean–Cano wedge in relation to the anchoring strength and mutual orientation of the easy axes at the wedge surfaces are performed for various model surface anchoring potentials. Comparison of the theory and experiment allows one to propose the socalled model D-potential, quadratic in angle of director deviation from the easy axes, as the best one in fitting the experiment in the angular range of performed measurements. To satisfy general requirements on the wedge surface, a modified D-potential is proposed. The optimal conditions of the experiment aimed at restoring the potential in the whole range of its definition (in particular, nonparallel orientation of the easy axes at the wedge surfaces) are formulated.     

Structures and thermoelectric convection in cholesteric liquid crystals

The possibilities for excitation of electromagnetic field structures and convection cells, i.e., temperature and velocity structures, in a thermotropic cholesteric liquid crystal in the presence of flow are studied. Estimates are made and possible experiments for observing such structures are discussed. A special thermoelectric effect is investigated as the cause of these excitations — the influence of a heating-induced change in the pitch of the cholesteric helix of the molecules on the permittivity and the electric conductivity of the material. Fiz. Tverd. Tela (St. Petersburg) 41, 165–170 (January 1999)     

Nonlinear “brightening” of a film of nonabsorbing chiral nematic under selective reflection conditions

A strong decrease in the reflection coefficient of a film of a nonabsorbing chiral nematic (cholesteric) is observed experimentally in the region of selective reflection under the action of a powerful beam of circularly polarized light. The independence of the effect from the average power density (and its dependence only on the peak power density) allow it to be attributed to an increase in the pitch of the cholesteric helix to such a degree that it is completely unwound, an effect previously observed only in static and low-frequency electric and magnetic fields, in the strong field of the light wave. These are the first experiments in which, on account of the specially chosen irradiation conditions, the changes produced in the pitch of the helix by the field of the light wave can accumulate over time, so that a nonthermal mechanism can be invoked to explain the nonlinear brightening of a mirror made of a chiral nematic. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 403–407 (25 March 1996)