W. Jeżewski

Non-linear electrooptic effect in antiferroelectric liquid crystal

Electrooptic phenomena caused by weak electric fields, much lower than those needed for the helix unwinding, in helical smectic liquid crystals were studied in thin planar samples. The investigations were performed in chiral liquid crystal 4-(1-methyl-heptyloxycarbonyl) phenyl 4′-(3-butanoyloxy propyl-1-oxy) biphenyl-4-carboxylate which exhibits antiferro-electric properties. We have found that electric field applied to a helical smectic liquid crystal caused two effects. First, the helix was deformed and the position of effective optic axis changed by an angle proportional to the field strength. The second effect, quadratic in field, causes the change in the shape of the indicatrix. As a consequence, the relative changes in the light intensity caused by external electric field consist of two components. The first component represents the modulation with the fundamental frequency and the second one with the doubled frequency (second harmonic of the electrooptic effect). The ab- solute values of the first- and second-order electrooptic coefficients have been determined and their temperature dependence discussed.

Dielectric relaxation in chevron surface stabilized ferroelectric liquid crystals

The dielectric response of surface stabilized ferroelectric liquid crystals with chevron layer structure is studied within low and intermediate frequency ranges, characteristic for collective molecular excitations. By analytically solving the dynamic equation for collective molecular fluctuations under a weak alternating electric field, it is demonstrated that chevron cells stabilized by both nonpolar and polar surface interactions undergo at medium frequencies two Debye relaxation processes, connected with two chevron slabs, on opposite sides of the interface plane. This result is confirmed, experimentally, making use of the electro-optic technique. Based on qualitative arguments supported by microscopic observations of zigzag defects at different frequencies and amplitudes of the external electric field, it is shown that, at low frequencies, the electro-optic response of chevron samples is determined by three kinds of motions of zigzag walls. The first two dynamic categories are related to collective relaxation processes at weak fields, within smectic A layers forming zigzag walls, and drift or creep motions of thick walls occurring at stronger field amplitudes. Dynamic processes of the third kind correspond to sliding of zigzag walls, which appear at yet stronger field amplitudes, but below the switching threshold.

Determination of twist elastic constant in antiferroelectric liquid crystals

An electro-optic method for determining the twist elastic coupling between smectic layers in antiferroelectric liquid crystals with a helical superstructure has been introduced. This method is based on a calibration procedure which enables a modulation of light intensity under an alternating applied electric field to relate to a respective modulation caused by mechanical oscillations of a sample. The elastic constant of antiferroelectric liquid-crystalline materials has been obtained by applying the method to a liquid crystal which displays a direct transition from antiferroelectric C*a phase to the smectic A phase.

Field-induced dynamics of ferroelectric liquid crystals with elastic interfacial confinement

Dynamic properties of surface stabilized ferroelectric liquid crystals driven by an alternating external electric field and confined inside measuring cells by air are studied. Using the electro-optic response method, it has been possible to register response spectra of small parts of liquid crystals near surfaces of their contact with air. This has allowed the direct determination of the dependence of changes of such partial electro-optic response spectra on the distance of illuminated liquid-crystal areas from the contact surfaces. The interfacial dynamic processes are found to enhance considerably the electro-optic response over relatively large distances from contact surfaces, within a wide range of field frequencies. Experimental data obtained from the used approach to determine the fragmentary electro-optic response indicate that the approach can be very effective for studying various interfacial phenomena in thin liquid-crystal systems.

Dielectric versus optical response of chevron ferroelectric liquid crystals

Dielectric and optical methods to investigate the response of surface‐stabilized ferroelectric liquid crystals (SSFLCs) of the chevron structure are examined and compared in the case of the azimuthal mode of collective relaxation processes. It is found that the variation of an effective (averaged over the chevron cell volume) dielectric permittivity tensor under the influence of a weak alternating external electric field is approximately equivalent to the transformation of this tensor as a consequence of the rotation of the laboratory frame around the axis perpendicular to the smectic plane about a small angle. Then, using an analytic solution of the equation of motion describing the azimuthal rotation of molecules, it is shown that both of the analysed approaches to calculate and measure the response of SSFLCs yield consistent results for these rotational dynamic processes. This allows the calculation of the spontaneous polarization of the unit volume of chevron slabs, provided that the pretilted azimuthal angle (in the absence of an applied electric field) within the smectic plane is known.

Electric-field-induced weakly chaotic transients in ferroelectric liquid crystals.

Nonlinear dynamics induced in surface stabilized ferroelectric liquid crystals by strong alternating external electric fields is studied both theoretically and experimentally. As has already been shown, molecular reorientations induced by sufficiently strong fields of high-enough frequencies can reveal a long transient behavior that has a weakly chaotic character. The resulting complex dynamics of ferroelectric liquid crystals can be considered not only as a consequence of irregular motions of particular molecules but also as a repercussion of a surface-enforced partial decorrelation of nonlinear molecular motions within smectic layers. To achieve more insight into the nature of this phenomenon and to show that the underlying complex field-induced behavior of smectic liquid crystals is not exceptional, ranges of system parameters for which the chaotic behavior occurs are determined. It is proved that there exists a large enough set of initial phase trajectory points, for which weakly chaotic long-time transitory phenomena occur, and, thereby, it is demonstrated that such a chaotic behavior can be regarded as being typical for strongly field-driven thin liquid crystal systems. Additionally, the influence of low-amplitude random noise on the duration of the transient processes is numerically studied. The strongly nonlinear contribution to the electro-optic response, experimentally determined for liquid crystal samples at frequencies lower than the actual field frequency, is also analyzed for long-time signal sequences. Using a statistical approach to distinguish numerically response signals of samples from noise generated by measuring devices, it is shown that the distribution of sample signals distinctly differs from the device noise. This evidently corroborates the occurrence of the nonlinear low-frequency effect, found earlier for different surface stabilized liquid crystal samples.

Strongly nonlinear dynamics of ferroelectric liquid crystals

Molecular reorientation processes induced in thin ferroelectric liquid crystal systems by strong alternating external electric fields are studied both by solving numerically the equation of reorientation motion of molecules and by measuring the electro-optic response of thin samples. It is shown that the occurrence of a wide band in nonlinear response spectra above the Goldstone-mode frequency is a consequence of complex partially uncorrelated molecular reorientations enforced within smectic layers by sufficiently high fields of high enough frequencies. Such nonlinear reorientational motions of molecules are argued to have a character of weakly chaotic long-lasting transients, related to almost periodic modulations of the amplitude of rotational oscillations performed by molecules with the field frequency. These modulations have been numerically proved to proceed with lower frequencies than the field frequency and with space-dependent depths of temporal changes. The occurrence of the modulations has experimentally been confirmed by registering distinct contributions to electro-optic response spectra at frequencies less than the running frequency of the applied electric field.Graphical abstract

Comparison of methods for determination of viscoelastic properties in chiral smectics C

The knowledge of the material parameters related to the microscopic structure of liquid crystals is one of the main problems in the construction of the liquid crystal devices. In the case of ferroelectric liquid crystals, the viscoelastic properties are very important as they determine the switching speed and the threshold voltage in displays. There exist several experimental methods for measurements of viscosity and elasticity constants in tilted smectic phases which exploit various phenomena for deformation detection, e.g., light transmission, polarization current, light modulation, dielectric constant, and helix deformation or helix unwinding. In this article, we compared the results of measurements obtained for the same material using various methods. The experiments proved that the correct bulk values of the mentioned material constants can be determined using thick, homeotropically aligned samples only.

Solitons in surface stabilized ferroelectric liquid crystals and the determination of the twist elastic constant

Excitation of solitary waves and their propagation in surface-stabilized ferroelectric liquid crystal cells under alternating external electric field is investigated both theoretically and experimentally. The effect of solitary waves on electro-optic response spectra is analyzed for different amplitudes of applied fields, temperatures, and sample thicknesses. It is shown that solitons can only be excited within narrow ranges of frequencies of the sufficiently strong electric fields. The minimal frequency, at which soliton waves appear in ferroelectric smectic liquid crystals, is found to be related to the material constants of these systems. It is proved that measuring this threshold frequency gives the possibility to determine one of the material parameters, if the others are known. In this way, the intra-smectic-layer elastic constant is found for systems with the chevron geometry.

Determination of bulk values of twist elasticity coefficient in a chiral smectic C* liquid crystal

A method is described for determination of bulk values of a twist elastic coefficient for smectic c-director in chiral smectic liquid crystals with a helical structure. The method was applied to 4-methylbutyloxy phenyl-4-octyloxy-benzoate (C8) in the chiral smectic C* phase. The measurements were performed using optical detection in a small deformation limit. In contrast to the usual methods, initial deformation of the helix (caused by strong surface interactions) was avoided by using homeotropic aligned thick samples. The critical temperature dependence of the measured coefficient was observed. The relation between the measured parameter and the smectic C order parameter is presented.