Saddle-splay-term-induced orientational instability in nematic-liquid-crystal cells and director fluctuations at substrates

Influence of flexoelectric effect on the Fréedericksz transition in chiral nematic liquid crystals

Electric field driven Frèedericksz transition in chiral nematic (cholesteric) planar liquid crystal cell is studied in the presence of flexoelectric effect. An inhomogeneity of electric field and finiteness of anchoring energy are considered. The extra contribution to the electric field induced by flexoelectricity is taken into account as well as the common contribution arising from the applied voltage U. Equilibrium director distribution is obtained in dependence on voltage and flexoelectric coefficients by numerical minimization of the free energy. The threshold voltage was found to decrease with the increase of the flexoelectric coefficients within the range of high flexoelectric coefficients. Thus flexoelectricity promotes the transition. The orientational structure becomes asymmetric about the center of the cell due to flexoelectricity, even in the case of symmetric boundary conditions. The equilibrium structure was also shown to be different for U>0 and U<0. It was found, that for sufficiently high flexoelectric coefficients the director distribution can be described by a simple function. In this case the planar helicoidal structure transfers into a hybrid-aligned one as the voltage increases. This transformation may form the basis for new flexoelectricity-based switching devices. The nonmonotonic behavior of threshold voltage can be observed in the case of small flexoelectric coefficients. An analytical form of the stability conditions was obtained for the planar helicoidal configuration. We have shown that the Frèedericksz transition can be either continuous or discontinuous depending on the material constants and thickness of the liquid crystal cell.

First-order and continuous Fréedericksz transitions in cholesteric liquid crystals

The Fréedericksz transition in twist cells of cholesteric liquid crystals with a finite surface energy is considered. It is shown that this transition can be either of the second order or of the first order depending on the values of the Frank constants, pitch, surface energies, and the cell thickness. A simple criterion that determines the order of the phase transition is obtained. By numerically minimizing the free energy of the liquid-crystal pattern the distribution of the director in the presence of the external electric field is calculated. For this purpose the polar angle of the director was presented as a partial sum of the Fourier series and of the appropriate function. The azimuthal angle was eliminated using Euler-Lagrange equations. Calculations were performed for different sets of liquid-crystal parameters which provide the phase transition of the first and of the second order. The numerical results are in a good agreement with theoretical formulas based on the Landau-type theory.

Thin nematic films on liquid substrates

Thin films of cyanobiphenyl liquid crystals (nCB) deposited on water or glycerol have been studied in the nematic temperature range. A common property of the systems is the hybrid anchoring conditions at the film interfaces. The preferred orientation of the nematic director is planar at the liquid interface, and it is homeotropic and somewhat weaker at the air interface. The resulting structure of the film depends on its thickness. Films thicker than 0.5 microm show the usual defects of nematics. Between 0.5 microm and 20-30 nm, complex instability patterns such as stripes, "chevrons", or squares are observed in extended films. Then there is a forbidden range of thickness below in which much thinner structures (usually monolayers and trilayers) are present. The present paper investigates this common behavior in various systems and gives arguments for its analysis.

Periodic saddle-splay Freedericksz transition in nematic liquid crystals

By use of a local stability criterion recently introduced, we predict the existence of a periodic saddle-splay Freedericksz (PSSF) transition that adds to the existing class of classical Freedericksz transitions driven in a nematic cell by an external field. Occurrence of the PSSF transition requires a saddle-splay elastic constant with a large enough magnitude and different anchoring strengths at the plates confining the nematic cell. Otherwise, either the PSSF transition does not occur at all, or it requires a field higher than that associated with the classical aperiodic splay Freedericksz (ASF) transition, in which case it is not observable. Here, we determine the threshold field for which the PSSF precedes the ASF transition, as well as the structure of the destabilizing mode.

Twist of cholesteric liquid crystal cells: stability of helical structures and anchoring energy effects

We consider helical configurations of a cholesteric liquid crystal (CLC) sandwiched between two substrates with homogeneous director orientation favored at both confining plates. We study the CLC twist wave number q characterizing the helical structures in relation to the free twisting number q(0) which determines the equilibrium value of CLC pitch P(0) = 2 pi/ q(0) . We investigate the instability mechanism underlying transitions between helical structures with different spiral half-turn numbers. Stability analysis shows that for equal finite anchoring strengths this mechanism can be dominated by in-plane director fluctuations. In this case the metastable helical configurations are separated by the energy barriers and the transitions can be described as the director slippage through these barriers. We extend our analysis to the case of an asymmetric CLC cell in which the anchoring strengths at the two substrates are different. The asymmetry introduces two qualitatively different effects: (a) the intervals of twist wave numbers representing locally stable configurations with adjacent helix half-turn numbers are now separated by instability gaps; and (b) sufficiently large asymmetry, when the difference between azimuthal anchoring extrapolation lengths exceeds the thickness of the cell, will suppress the jumplike behavior of the twist wave number.