Short-Pitch Modes Approach to the Problem of Antiferroelectricity in Liquid Crystals

Resonant X-ray Scattering: A Tool for Structure Elucidation in Liquid Crystals

The use of resonant X-ray scattering to determine structures in liquid crystal systems is surveyed. This powerful experimental technique utilises "forbidden reflections" to determine the subtle differences in interlayer orientation that differentiate several smectic systems. The technique relies on the materials containing an atom to which the X-ray energy can be tuned, usually sulphur or selenium. Experiments are often carried out on free-standing films that provide a highly monodomain structure that allows high-resolution measurements to be made, and, hence, structural details to be determined. Alternatively, resonant scattering has been demonstrated for materials contained in glass devices that permit the application of electric fields to the system, in a manner analogous to that used in liquid crystal devices. The resonant scattering technique provides unequivocal descriptions of the packing in smectic systems, and the way in which the packing is distorted in electric fields. This Minireview describes the principles behind resonant X-ray scattering, its application to liquid crystals and some of the potential for the future.

Two kinds of smectic-C(alpha)* subphases in a liquid crystal and their relative stability dependent on the enantiomeric excess as elucidated by electric-field-induced birefringence experiment

The electric-field-induced birefringence has been investigated by using a photoelastic modulator, with a view to obtaining a molecular model for the subphases produced by the frustration between ferroelectricity and antiferroelectricity in the chiral smectic liquid crystals. It has been found that even in the bulk, there exist two subphases in the smectic-C(alpha)* (Sm-C(alpha)*) temperature range. By extending the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)] to include the temperature dependence of the tilt angle, we have alluded to a possible lifting of the degeneracy at the frustration point P(alpha) , where Sm-C(A)*, Sm-C*, and Sm-A have the same free energy. This leads to the appearance of uniaxial Sm-C(alpha)* characterized by short-pitch helical structures and consequently with a pitch much lower than the optical wavelength. The numerical calculations indicate that the short pitch may generally increase or decrease monotonically with temperature. Depending on the parameter value that represents the relative strength of ferroelectricity and antiferroelectricity, the short-pitch temperature variation may abruptly change from increase to decrease at a temperature; this can be assigned to the observed phase transition between the two Sm-C(alpha)* subphases.

Structures and phase transitions in polar smectic liquid crystals

A discrete phenomenological model of antiferroelectric liquid crystals is used to study the structures and phase transitions in bulk samples and thin films. An important ingredient of our investigations is minimization of the free energy with respect to the phase and modulus of the order parameter. A simple version of the free energy, which contains only the nearest-neighbor and the next-nearest-neighbor layer interactions gives a complete phase diagram with all the observed smectic-C* (SmC*) variant phases. In thin free-standing films, surface ordering may lead to suppression of the bulk SmC(*)(alpha) helix and to formation of planar structures. Transitions between these structures are accompanied by the 90 degrees reorientation of the polarization direction. We also discuss the influence of chirality on subphase structures.

Interlayer structures of the chiral smectic liquid crystal phases revealed by resonant X-ray scattering

The structures of the liquid crystalline chiral subphases exhibited by several materials containing either a selenium or sulphur atom have been investigated using a resonant x-ray scattering technique. This technique provides a unique structural probe for the ferroelectric, ferrielectric, antiferroelectric, and SmC(*)(alpha) phases. An analysis of the scattering features allows the structural models of the different subphases to be distinguished, in addition to providing a measurement of the helical pitch. This paper reports resonant scattering features in the antiferroelectric hexatic phase, the three- and four-layer intermediate phases, the antiferroelectric and ferroelectric phases and the SmC(*)(alpha) phase. The helicoidal pitch has been measured from the scattering peaks in the four-layer intermediate phase as well as in the antiferroelectric and ferroelectric phases. In the SmC(*)(alpha) phase, an investigation into the helical structure has revealed a pitch ranging from 5 to 54 layers in different materials. Further, a strong resonant scattering signal has been observed in mixtures of a selenium containing material with as much as 90% nonresonant material.

Dielectric investigation of electrically oriented ferroelectric smectic mixture CS-1013

From dielectric spectroscopic study, a first-order ferroelectric phase transition has been observed in ferroelectric smectic mixture CS-1013 having the phase sequence Cr-SmC*-SmA-N*-Iso. Frequency (100 Hz-10 MHz) and temperature-dependent dielectric measurements have been performed on an electrically aligned sample (thickness 15+/-1 microm) gold coated on glass plates. In the unidirectionally aligned sample, two dielectric relaxation modes (Goldstone mode and soft mode) have been clearly observed in the ferroelectric SmC* phase while only one relaxation mode (soft mode) is visualized in the paraelectric SmA phase. Low-frequency molecular relaxation was also observed in the smectic phases. The experimental results have also been analyzed at different temperatures and biasing voltages for an understanding of the dynamics of dielectric processes in the ferroelectric phase. Finally, we proposed the "pseudospin" model for understanding the ferroelectric-antiferroelectric transition in liquid crystals. We associate the tilt angle straight theta and the pitch of the helix, respectively, with biaxial (b) and uniaxial (u) anisotropy parameters as fluctuating parameters around their stability limit (corresponding to the crystalline values). Here, the director acts as the pseudospin variable. This gives rise to a transverse Ising type (or anisotropic Heisenberg model under the mean-field approximation). It is then shown that such a model with fluctuations of (b) and (u) would explain the ferroelectric and antiferroelectric phase transitions in such liquid crystals. Using Landau theory and the stability conditions, we have also shown, in brief, the feasibility of different types of phase transitions in the ferroelectric liquid crystal system.

Structure of freely suspended chiral smectic films as determined by x-ray reflectivity and optical ellipsometry

We report on a combined x-ray reflectivity and optical ellipsometry study of freely suspended smectic (Sm) films of a chiral liquid crystalline compound with the phase sequence Sm-A-Sm-C(*)(alpha)-Sm-C*-Sm-C(*)(gamma)-Sm-C(*)(A). Using tilt magnitude profiles from x-ray reflectivity as input to model the average optical properties obtained by ellipsometry, tilt direction profiles are also obtained. In this way realistic models can be elaborated for the various types of chiral Sm-C films. We find that the surface layers are more tilted than the interior layers due to surface interactions and finite size effects. For the ferrielectric Sm-C(*)(gamma) phase the tilt direction profile corresponds to a three-layer helix, in agreement with the clock model of chiral Sm-C phases. In thin films the surface interactions suppress the bulk helix structure of the Sm-C(*)(alpha) phase and a Sm-C(*)(A)-like structure is formed with an anticlinic layer-by-layer alternation of the tilt directions.

Resonant x-ray scattering study of the antiferroelectric and ferrielectric phases in liquid crystal devices

Resonant x-ray scattering has been used to investigate the interlayer ordering of the antiferroelectric and ferrielectric smectic C* subphases in a device geometry. The liquid crystalline materials studied contain a selenium atom and the experiments were carried out at the selenium K edge allowing x-ray transmission through glass. The resonant scattering peaks associated with the antiferroelectric phase were observed in two devices containing different materials. It was observed that the electric-field-induced antiferroelectric to ferroelectric transition coincides with the chevron to bookshelf transition in one of the devices. Observation of the splitting of the antiferroelectric resonant peaks as a function of applied field also confirmed that no helical unwinding occurs at fields lower than the chevron to bookshelf threshold. Resonant features associated with the four-layer ferrielectric liquid crystal phase were observed in a device geometry. Monitoring the electric field dependence of these ferrielectric resonant peaks showed that the chevron to bookshelf transition occurs at a lower applied field than the ferrielectric to ferroelectric switching transition.

Unusual thickness-dependent thermal behavior and anticlinic coupling in chiral smectic free-standing liquid-crystal films

We observe, in free-standing films of a chiral smectic liquid crystal, a series of discrete transitions in the relative orientation of the tilt of the interior and surface layers. These transitions include a remarkable reentrant synclinic-anticlinic-synclinic ordering sequence of the film surfaces in the presence of an electric field upon cooling. The profiles of the associated heat-capacity anomalies are found to be strongly thickness dependent and exhibit a novel crossover behavior in reduced dimensions. We measure the anticlinic coupling between tilted surface layers in the smectic- A phase.

Structure of the liquid-crystal ferrielectric phases as determined by ellipsometry

The unit cell structures of two ferrielectric liquid-crystal phases are determined from ellipsometric studies of freestanding films in a nondistorting rotatable electric field. A highly biaxial mode with out-of-plane distortions describes all of the data from two different compounds. Qualitative and quantitative features of the data rule out alternate models. We also present a detailed explanation for apparent inconsistencies between previous resonant x-ray and optical experiments.

Structure of the chiral smectic-C(*)(alpha) phase

Ellipsometric measurements of freely suspended films of a chiral liquid-crystal compound possessing the phase sequence smectic-A-smectic-C(*)(alpha)-smectic-C* have been conducted in order to elucidate the structure of the smectic-C(*)(alpha) phase. The measured ellipsometric quantities Delta and Psi are compared with values, which were calculated for model films using the 4x4 matrix method. Our results confirm, for the compound under investigation, predictions of a phenomenological model [M. Cepic and B. Zeks, Mol. Cryst. Liq. Cryst. 263, 61 (1995)] according to which the smectic-C(*)(alpha) phase is characterized by a short-pitch helical structure.

Structures of chiral smectic-C mesophases revealed by polarization-analyzed resonant x-ray scattering

We report polarization-analyzed, resonant x-ray diffraction at the sulfur K edge performed upon free-standing liquid-crystal films. Our studies of the thiobenzoate liquid-crystal enantiomer 10OTBBB1M7 yield the polarization states of resonant satellite peaks arising from characteristic superlattices in the chiral smectic-C (SmC(*)) variant phases, including the antiferroelectric SmC(*)(A), ferrielectric SmC(*)(FI1) and SmC(*)(FI2), as well as SmC(*)(alpha). The observed polarizations agree with the clock model of chiral smectic-C variants, and rule out other proposals made to date for these structures. Data from the 10OTBBB1M7 racemate also support the clock model. Our resonant diffraction results from a thiophene liquid-crystal compound reveal the same superlattice periodicities seen in corresponding antiferroelectric and ferrielectric phases of 10OTBBB1M7.

Tensorial x-ray structure factor in smectic liquid crystals

The amplitudes and the polarizations of the different resonant reflections characterizing the modulation of the orientational order in smectic liquid crystals are derived from the molecular tensorial structure factor. In the case of a commensurate helicoidal modulation, our conclusions are consistent with the previous predictions of Dimitrienko. We have extended Dimitrienko's prediction to incommensurate helicoidal structures and to commensurate but nonhelicoidal modulations. We have compared the estimated values for different models of modulations with the same period, with the experimental data obtained on different smectic-C variants. These comparisons enable us to discriminate between the different models.

A novel property caused by frustration between ferroelectricity and antiferroelectricity and its application to liquid crystal displays-frustoelectricity and V-shaped switching

We have studied the frustration between ferro- and antiferro-electricity in chiral smectic C like liquid crystalline phases, which is not only fundamentally interesting but also very attractive from an application point of view. It causes temperature induced successive phase transitions as characterized by a devil's staircase and the thresholdless, hysteresis-free, V-shaped switching induced by an applied electric field. The devil's staircase indicates some type of interlayer ordering, while the V-shaped switching suggests considerably diminished tilting correlation. These two are apparently contradictory to each other, but result from the same cause, i.e. the frustration. We have first summarized experimental facts regarding subphases and successive phase transitions observed in many compounds and mixtures, which we believe are related to one another and result from the frustration. We have introduced several different theoretical explanations for these observed facts, and shown that only the axial next nearest neighbor Ising (ANNNI) model can explain almost all of the facts, provided that it is unified with the XY model appropriately. The unified model can make a comprehensive explanation in the most natural way based on the most probable molecular interactions. We have then emphasised that there are several modes regarding the V-shaped switching, because the system becomes so soft with respect to the tilting direction and sense that any additional external or internal force modifies the in-plane local director alignments. For the practically usable ones, we have emphasised the need for some type of randomization in the molecular alignment at the tip of the V and/or the switching process. In particular, the two dimensional (ideally, cylindrically symmetric) azimuthal angle distribution of local in-plane directors around the smectic layer normal is most attractive. Such a randomized state at the tip of the V is thermodynamically unique under a given condition imposed by interfaces. It stays stable even when the smectic layer structure, such as a chevron, changes with temperature. Finally, we have summarized the so-far reported compounds and mixtures for the V-shaped switching and introduced some prototypes of LCDs using them.