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

Ultra-short helix pitch and spiral ordering in cholesteric liquid crystal revealed by resonant soft X-ray scattering

The spontaneous formation of chiral structures offers a variety of liquid crystals (LC) phases that could be further tailored for practical applications. In our work, the characteristic features of spiral ordering in the cholesteric phase of EZL10/10 LC were evaluated. To disclose resonant reflections related to a nanoscale helix pitch, resonant soft X-ray scattering at the carbon K edge was employed. The angular positions of the observed element-specific scattering peaks reveal a half-pitch of the spiral ordering p/2 ≈ 52 nm indicating the full pitch of about 104 nm at room temperature. The broadening of the peaks points to a presence of coherently scattering finite-size domains formed by cholesteric spirals with lengths of about five pitches. No scattering peaks were detectable in the EZL10/10 isotropic phase at higher temperatures. The characteristic lengths extracted from the resonant soft X-ray scattering experiment agree well with the periodicity of the surface "fingerprint" pattern observed in the EZL10/10 cholesteric phase by means of atomic force microscopy. The stability of LC molecules under the incident beam was proven by X-ray absorption spectroscopy in transmission geometry.

Chiral Symmetry Breaking in Liquid Crystals: Appearance of Ferroelectricity and Antiferroelectricity

The study of chiral symmetry breaking in liquid crystals and the consequent emergence of ferroelectric and antiferroelectric phases is described. Furthermore, we show that the frustration between two phases induces a variety of structural phases called subphases and that resonant X-ray scattering is a powerful tool for the structural analysis of these complicated subphases. Finally, we discuss the future prospects for clarifying the origin of such successive phase transition.

Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X-Ray Scattering

Intensive research on chiral liquid crystals (LCs) has been fueled by their actively tunable physicochemical properties and structural complexity, comparable to those of sophisticated natural materials. Herein, recent progress in the discovery of new classes of chiral LCs, enabled by a combination of nano- and macroscale investigations is reviewed. First, an overview is provided of liquid crystalline phases, made of chiral and achiral low-weight molecules, that exhibit chiral structure and/or chiral morphology. Then, recent progress in the discovery of new classes of chiral LCs, particularly enabled by the application of resonant X-ray scattering is described. It is shown that the method is sensitive to modulations of molecular orientation and therefore provides information hardly accessible by means of other techniques, such as the sense of helical structures or chirality transfer across length scales. Finally, a perspective is presented on the future scope, opportunities, and challenges in the field of chiral LCs, in particular related to nanocomposites.

Pseudopolar smectic-C phases of azo-substituted achiral bent-core hockey-stick-shaped molecules

We report experimental studies on an azo-substituted compound consisting of bent-core hockey-stick-shaped molecules. The experimental results establish two pseudopolar tilted smectic phases, which are characterized by an in-plane axial-vector order parameter in addition to tilt order in the smectic layers. Electro-optical measurements in the mesophases indicate that the birefringence of the sample strongly depends on the applied electric field. We develop a theoretical model to account for this observation. The change in the birefringence of the sample arises from the field-induced reorientation of the tilt plane of the molecules in the layer above a threshold field. The effect is analogous to the field-induced Freedericksz transition which is quadratic in the applied electric field.

Unexpected electric-field-induced antiferroelectric liquid crystal phase in the SmC_{α}^{*} temperature range and the discrete flexoelectric effect

The unique nanometer-sized helical structure in SmC_{α}^{*} may sometimes evolve continuously to the micrometer-sized one in SmC^{*}; conceivably ferroelectric SmC_{α}^{*} is to be unwound by an applied electric field. By drawing electric-field-induced birefringence contours in the field-temperature phase diagram and by studying the superlattice structure of the field-induced subphase with resonant x-ray scattering, we established that an applied field unexpectedly stabilizes the well-known antiferroelectric four-layer biaxial subphase as well as the other prototypal ferrielectric three-layer one in the SmC_{α}^{*} temperature range; the effective long-range interlayer interaction due to the discrete flexoelectric effect actually plays an important role in stabilizing not only the biaxial subphases but also the optically uniaxial SmC_{α}^{*} subphase, contrary to the notion that the competition between the direct interactions of the nearest-neighbor layers and those of the next-nearest-neighbor layers should be required for the nanometer-sized helical structure.

Resonant x-ray scattering observation of transitional subphases during the electric-field-induced phase transition in a mixture of Se-containing chiral smectic liquid crystals

Using resonant x-ray scattering techniques, transitional subphases during the electric-field-induced phase transition of a mixture of Se-containing chiral liquid crystals, 80% AS657 and 20% AS620, in a planar-aligned cell geometry were investigated, where the prototypical phase sequence SmC_{A}^{*}-SmC_{γ}^{*}-AF-SmC^{*} was observed; the transitional subphases were formed during the transition from the three-layer periodicity phase to the ferroelectric phase. In the lower-temperature range where the three-layer SmCγ^{*} phase appeared under the low electric field, nine- and six-layer subphases and a "streak" pattern appeared in sequence after the transition from the SmCγ^{*} phase with increasing applied electric field; the ferroelectric phase was realized. In the higher-temperature range where the four-layer AF phase appeared under a low electric field, the AF phase changed to a three-layer phase at the medium electric field. The twelve-, nine-, and six-layer subphases subsequently appeared in sequence, and finally the ferroelectric phase was generated with increasing electric field. The molecular arrangements of the field-induced subphases, especially the newly found nine-layer periodicity phase, was analyzed. The successive field-induced phase transition of the present results was compared with that of our previous results for pure Se-containing and Br-containing liquid crystals, and the relation to the three-layer ferrielectric phase was discussed.

Definite existence of subphases with eight- and ten-layer unit cells as studied by complementary methods, electric-field-induced birefringence and microbeam resonant x-ray scattering

A mixture of two selenium-containing compounds, 80 wt. % AS657 and 20 wt. % AS620, are studied with two complementary methods, electric-field-induced birefringence (EFIB) and microbeam resonant x-ray scattering (μRXS). The mixture shows the typical phase sequence of Sm-C_{A}^{*}-1/3-1/2-Sm-C^{*}-Sm-C_{α}^{*}-Sm-A, where 1/3 and 1/2 are two prototypal ferrielectric and antiferroelectric subphases with three- and four-layer unit cells, respectively. Here we designate the subphase as its q_{T} number defined by the ratio of [F]/([F]+[A]), where [F] and [A] are the numbers of synclinic ferroelectric and anticlinic antiferroelectric orderings in the unit cell, respectively. The electric field vs temperature phase diagram with EFIB contours indicates the emergence of three additional subphases, an antiferroelectric one between Sm-C_{A}^{*} and 1/3 and antiferroelectric and apparently ferrielectric ones between 1/3 and 1/2. The simplest probable q_{T}'s for these additional subphases are 1/4, 2/5, and 3/7, respectively, in the order of increasing temperature. The μRXS profiles indicate that antiferroelectric 1/4 and 2/5 approximately have the eight-layer (FAAAFAAA) and ten-layer (FAFAAFAFAA) Ising unit cells, respectively. The remaining subphase may be ferrielectric 3/7 with a seven-layer unit cell, although the evidence is partial. These experimental results are compared with the phenomenological Landau model [P. V. Dolganov and E. I. Kats, Liq. Cryst. Rev. 1, 127 (2014)2168-039610.1080/21680396.2013.869667] and the quasimolecular model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)1063-651X10.1103/PhysRevE.68.051703].

Transitional subphases near the electric-field-induced phase transition to the ferroelectric phase in Se-containing chiral smectic liquid crystals observed by resonant x-ray scattering

Resonant x-ray scattering experiments revealed transitional subphases near the electric-field-induced phase transition of a Se-containing chiral liquid crystal in a planar aligned cell geometry. In the lower-temperature range (Sm-C_{A}^{*} and three-layer periodicity Sm-C_{γ}^{*} phases), the six-layer periodicity subphase appeared with increasing electric field during the field-induced transition from Sm-C_{γ}^{*} to Sm-C^{*}. In the higher-temperature range [four-layer periodicity antiferroelectric (AF) phase], the peak positions of the three-layer satellites shifted to those of the four-layer satellites and then the satellites corresponding to the five- through seven-layer periodicity appeared in sequence. Near the AF to Sm-C_{α}^{*} phase transition temperature, the layer periodicity increased with applied field. The molecular configurations of the subphases near the field-induced transition are discussed based on the Ising, distorted clock, and perfect clock models.

Resonant Carbon K-Edge Soft X-Ray Scattering from Lattice-Free Heliconical Molecular Ordering: Soft Dilative Elasticity of the Twist-Bend Liquid Crystal Phase

Resonant x-ray scattering shows that the bulk structure of the twist-bend liquid crystal phase, recently discovered in bent molecular dimers, has spatial periodicity without electron density modulation, indicating a lattice-free heliconical nematic precession of orientation that has helical glide symmetry. In situ study of the bulk helix texture of the dimer CB7CB shows an elastically confined temperature-dependent minimum helix pitch, but a remarkable elastic softness of pitch in response to dilative stresses. Scattering from the helix is not detectable in the higher temperature nematic phase.

Probing and controlling liquid crystal helical nanofilaments

We report the first in situ measurement of the helical pitch of the helical nanofilament B4 phase of bent-core liquid crystals using linearly polarized, resonant soft X-ray scattering at the carbon K-edge. A strong, anisotropic scattering peak corresponding to the half-pitch of the twisted smectic layer structure was observed. The equilibrium helical half-pitch of NOBOW is found to be 120 nm, essentially independent of temperature. However, the helical pitch can be tuned by mixing guest organic molecules with the bent-core host, followed by thermal annealing.

Understanding the unusual reorganization of the nanostructure of a dark conglomerate phase

The dark conglomerate (DC) phase exhibited by a bent-core liquid crystal shows remarkable properties including an electric-field tunable chiral domain structure and a large (0.045) reduction of refractive index, while maintaining an optically dark texture when observed under crossed polarizers. A detailed investigation of the system is presented, leading to a model that is fully consistent with the experimental observations. It reports the observation of two distinct regimes in the DC phase: a higher temperature regime in which the periodicity measured by small angle x-ray scattering decreases slightly (0.5%) and a lower temperature regime where it increases considerably (16%). Also, the paper discusses the unusual electric-field-induced transformations observed in both the regimes. These changes have threshold fields that are both temperature and frequency dependent, though the phenomena are observed irrespective of device thickness, geometry, and the alignment layer. The electro-optic behavior in the DC phase corresponds to a number of structural changes leading to unusual changes in physical properties including a small (1%) increase in periodicity and a doubling of the average dielectric permittivity. We propose a model of the DC phase where in the ground state the nanostructure of the phase exhibits an anticlinic antiferroelectric organization. Under an electric field, it undergoes a molecular rearrangement without any gross structural changes leading to an anticlinic ferroelectric order while keeping the overall sponge-like structure of the DC phase intact.

Chiral smectic transition phases appearing near the electric-field-induced phase transition observed by resonant microbeam x-ray scattering

The electric-field-induced phase transition of a chiral liquid crystal containing Br revealed a transition phase between the three-layer periodicity ferrielectric phase and the synclinic ferroelectric phase in the electric field versus temperature phase diagram. Resonant x-ray scattering from the transition phase showed a diffuse streak or spotty weak reflections, which were composed of strong m/3-order (where m = 1 and 2) reflections and other weak peaks. The spotty reflections were found to be related to a 12-layer periodicity phase with a weak contribution from the 15-layer periodicity. An x-ray intensity analysis based on the Ising model suggested that the 12-layer periodicity phase was composed of two three-layer ferrielectric blocks and six synclinic layers. This model indicated that, in the transition phase, the three-layer ferrielectric molecular configuration gradually changed to the synclinic configuration. The diffuse streak appearing around m/3-order reflections near the field-induced transition from the four-layer periodicity phase to the synclinic ferroelectric phase is also discussed.

Smectic-C* liquid crystals with six-layer periodicity appearing between the ferroelectric and antiferroelectric chiral smectic phases

We found a subphase with a six-layer periodicity which appears between the ferroelectric SmC(*) and the antiferroelectric SmC(A)(*)(q(T) = 0) phases. The six-layer periodic structure is directly determined by the microbeam resonant x-ray scattering measurement. Furthermore, considering the dielectric constants, this phase was found to be ferrielectric, assigned as SmC(A)(*)(q(T) = 2/3). This subphase indicates the importance of the competition between the ferro- and the antiferroelectric phases and, in that point, it is essentially different from the previously observed six-layer phase. The relation between current theories and our present experimental results has been studied and discussed.

Theory for the evolution of ferroelectric, antiferroelectric, and ferrielectric smectic phases in the electric field

An evolution of Sm-C(A)∗, biaxial intermediate phases, and Sm-C∗ in the electric field is investigated in a framework of molecular-statistical approach [A. V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006); A. V. Emelyanenko, Eur. Phys. J. E 28, 441 (2009)]. The "electric field-temperature" phase diagrams including the possibility of existence of various tilted smectic phases are plotted and compared with the experimental ones. Permanent transverse molecular dipole moments (without electric field participating only in the spontaneous polarization) were also found to generate the induced polarization in the presence of electric field and to produce very strong dielectriclike effect. This effect is positive in Sm-C∗ (tilt planes have a tendency of orienting along or against the electric field) and is negative in Sm-C(A)∗ and in biaxial intermediate phases (tilt planes have a tendency of orienting perpendicular to the electric field). In the ferrielectric intermediate phases both spontaneous and induced polarizations favor similar tendencies and provide the helix unwinding at very low electric field. At the same time, the tendencies provided by spontaneous and induced polarizations are opposite in Sm-C∗, and therefore the unwinding threshold is larger. It was shown that interplay between spontaneous and induced polarizations can lead to the formation of complex bidomain smectic structures. A single parameter regulating an evolution of structure of Sm-C∗, Sm-C(A)∗, and biaxial intermediate phases in the electric field was found. We suppose that bidomain helical structure is the same as additional ferrielectric phase FiLC existing in some materials just below Sm-C∗. The numerical calculations are done with help of AFLC phase diagram plotter software developed by the author and available at his webpage.

Microbeam resonant x-ray scattering from bromine-substituted bent-core liquid crystals

We studied the local layer structure in the B2 phase of bromine-substituted bent-core liquid crystals in the cell geometry using microbeam resonant x-ray scattering. In the homochiral state of B2 phase, the 3/2 order satellite peak was observed only when the incident x-ray energy is at the K absorption edge of bromine. This result clearly indicates that the B2 homochiral domain forms two-layer superlattice in adjacent layers, the same as in the rodlike Sm-C(A) phase. The work reports on microbeam resonant x-ray scattering experiment from the local layer of the bent-core liquid crystal in the device geometry. Moreover, we can say that bromine is also useful for the analysis of the superstructure of soft materials using resonant x-ray scattering.

Electric-field-dependent dielectric response in the de Vries-type smectic- A phase possessing local orientational order with nanoscale correlation length

The dielectric strength is shown to increase and the relaxation frequency to decrease for a large temperature range up to a certain value of the electric field in the smectic- A phase. This behavior contrasts to that observed in a conventional smectic- A , but can be explained in terms of de Vries scenerio. On assuming the reorientation of the molecular dipoles with electric field to be of the Langevin type in the de Vries smectic- A, we find that around 1,300 molecules , corresponding to a minimum correlation length of xi_{ perpendicular} approximately 45 nm in a single layer cooperatively respond to the applied field.

Effects of doping on an unusual smectic- C*alpha-smectic-C*FI2-smectic-C* phase sequence

The compound 10OHF has a partially inverted phase sequence, unique among the series of nOHF homologous compounds and all other known liquid crystals, with the smectic-C*FI2 (SmC*FI2) phase occurring at higher temperature than the smectic-C* (SmC*) phase. We present ellipsometric data to identify the phase sequences of 9OHF, 10OHF, 11OHF, and 12OHF. Binary mixtures of 10OHF with C11, a compound with the typical phase sequence among the smectic phases, show that the unusual phase sequence of 10OHF stabilizes upon mixing and that SmC*FI2 predominates over SmC* throughout the entire mixing phase diagram. In thin films of some mixtures, surface interactions induce a reentrant SmC*FI2-SmC*-SmC*FI2 transition in the rest of the film.

Electro-optic and dielectric study of the de Vries-type smectic-A* phase exhibiting transitions to smectic-C*A and smectic-C* phases

Mixtures of different compositions of an antiferroelectric liquid crystal compound that exhibits direct smectic-A*(Sm-A*)-smectic-C*(A) (Sm-C*(A)) transition with a ferroelectric liquid crystal compound that exhibits Sm-A*-smectic-C*(Sm-C*) transition are studied using electro-optics and dielectric spectroscopy. The results of optical texture, birefringence, and the tilt angle suggest that a part of the Sm-A* phase is of de Vries type, since an increase in the tilt angle with decreasing temperature results in a reduction in the value of the birefringence in the Sm-A* phase, whereas the birefringence at Sm-A* to Sm-C* transition goes up by 12.7%. The soft mode relaxation strength, the Landau coefficient of the temperature dependent term, and the other related parameters of the de Vries-type Sm-A-Sm-C*(A) and Sm-A*-Sm-C* transitions are determined using the Landau theory of the second-order phase transition. For the Sm-A*-Sm-C* transition, we find that the soft mode relaxation strength decreases, the Landau coefficient increases, and the Curie-Weiss temperature range decreases with an increased ferroelectric composition in the mixture. These observations can be explained by assuming that with increased ferroelectric composition in the mixture, the layer shrinkage at the de Vries Sm-A*-Sm-C* transition increases. On comparing the results of de Vries-type Sm-A* to Sm-C*(A) and Sm-C* transitions, we find that the soft mode dielectric strength and the other related Landau parameters of the de Vries Sm-A* phase are of the same order of magnitude for transitions from Sm-A* to Sm-C* and to Sm-C*(A) except for the composition of the mixture where both Sm-C* and Sm-C*(A) transitions are stable and the phase diagram shows phase sequence Sm-A* to Sm-C* to Sm-C*(A).

Unexpected field-induced phase transitions between ferrielectric and antiferroelectric liquid crystal structures

Liquid crystals are intriguing electrically responsive soft matter systems. We report previously unexplored field-induced changes in the structures of some frustrated liquid crystal phases and describe them theoretically. Specifically, we have discovered using resonant x-ray scattering that the four-layer intermediate smectic phase can undergo either a transition to the ferrielectric (three-layer) phase or to the ferroelectric phase, depending on temperature. Our studies of intermediate phases using electric fields offer a way to test theories that describe ferroelectricity in self-assembling fluids.

Extension of the resonant scattering technique to liquid crystals without resonant element

We report X-ray resonant scattering experiments performed on the prototype liquid-crystalline compound MHPOBC doped with a chemical probe containing a resonant atom (selenium). We determined directly for the first time the microscopic 3- and 4-layer structure of the ferrielectric subphases (SmC(FI1)* and SmC(FI2)*) present in MHPOBC. Despite the low fraction of the selenium probe, the resonant signal is strong enough to allow an unambiguous determination of the basic structure of the ferrielectric subphases. These experiments demonstrate that the resonant scattering technique can be extended to liquid crystalline materials without resonant element and may stimulate new studies. A non-resonant Bragg reflection was also found in the SmC(FI1)* phase in pure MHPOBC, consistent with the 3-layer distorted model, but never detected before.

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.

Discrete flexoelectric polarizations and biaxial subphases with periodicities other than three and four layers in chiral smectic liquid crystals frustrated between ferroelectricity and antiferroelectricity

The subphase for the temperature range that lies in between Sm-C(A)* and the three-layer Sm-C(A)* (1/3)subphase has been confirmed to exist using the measurements of electric-field-induced birefringence, optical rotation, and the characteristic reflection bands in the antiferroelectric liquid-crystalline compound, 1-trifluoromethylundecyl-4-(4'-dodecyloxybiphenyl-4-yl-carbonyloxy)-3-fluorobenzoate (12BIMF10). The measurements of electric-field-induced birefringence and optical rotatory power are made on -thick homeotropic cells, and the characteristic reflection bands are observed in free-standing films of thicknesses ranging from 30 to 50 microm. Several binary mixtures have been prepared by mixing (S)-12BIMF10 with (S)-4-(1-methylheptyloxycarbonyl)-phenyl-4'-octylbiphenyl-4-carboxylate (MHPBC), and the effect of racemization of the compound on the character of the biaxial subphase (other than three and four layers) is also discussed. The results are interpreted in terms of the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)]; the effective long-range couplings between the director orientations in separated smectic layers emerge after the minimization of free energy with respect to the total (ordinary spontaneous and discrete flexoelectric) polarizations, lifting the degeneracy and producing the nonplanar structures of the subphases.

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.

Evidence for different polymorphisms with and without an external electric field in a series of bent-shaped molecules

Five fluid tilted mesophases are observed in a series of achiral banana-shaped compounds. The terminal chain length is the pertinent molecular parameter which induces the polymorphism change. All the phases, refer to tilted lamellar structure without in-plane order in the layers. The observation of monolayer, bilayer, ribbon phase, and undulated structures recalls the richness of the polymorphism of the frustrated polar calamitic liquid crystals. Among the mesophases, we highlight two: a Sm-C G2 phase corresponding to a bilayer structure made of Sm-CG layers, and its two-dimensional variant, Sm- Ctilde; G2. The five mesophases observed at zero field are switchable under electric field. At least three ferroelectric phases are induced by an applied field. There is no direct correspondence between the zero field phases and the phases observed under electric field. These observations show that different polymorphisms exist in the series with and without an applied field. A unique ( E,T ) phase diagram is presented, corresponding to the superposition of the ( E,T ) diagrams obtained for each homolog of the series, where the influence of the chain length is equivalent to a shift on the temperature axis.

Self-assembled uniaxial and biaxial multilayer structures in chiral smectic liquid crystals frustrated between ferro- and antiferroelectricity

With a view to obtain a molecular model for the subphases produced by the frustration between ferro- and antiferroelectricity in chiral smectic liquid crystals, we report results on two compounds and observe (i) the staircase character of uniaxial Sm C(*)(alpha) itself in the bulk and (ii) the multipeaked characteristic reflection bands due to the modulated helical structures just above the Sm C(*)(A) temperature range. We suggest the emergence of several uniaxial and biaxial subphases. The results show that both types of subphases can be specified by q(T) = [F] / ( [A] + [F] ) in the zero-order approximation; [A] and [F] are the numbers of antiferroelectric and ferroelectric orderings in the unit cell. We consider the basis of both types of subphases, particularly the description of the short-pitch helical structure of Sm C(*)(alpha), in terms of the molecular models so far proposed and emphasize the important role played by the discrete flexoelectric polarization.

Antiferroelectric liquid-crystal mixture without smectic layer shrinkage at the direct Sm-A*-Sm-C(*)(a) transition

We report results of x-ray, optic, electro-optic, and dielectric investigations on an antiferroelectric liquid-crystal mixture exhibiting a direct second-order phase transition between the Sm-A* and Sm-C(*)(a) phases with virtually no shrinkage in the smectic layer spacing. The birefringence measurements and texture observations suggest that the phase transition follows the diffuse cone model of Adrian de Vries, which explains the constant layer spacing. The antiferroelectric nature of the tilted phase is verified by the presence of twin polarization reversal peaks in the current response and by the absence of strong absorptions in the dielectric spectrum. The threshold for switching this phase to the synclinic, ferroelectric state is sharp and occurs at a very low voltage.

Electroclinic effect and modulated phases in smectic liquid crystals

We explore the possibility that the unusually large electroclinic effect observed in the smectic-A phase of a ferroelectric liquid crystal arises from the presence of an ordered array of disclination lines and walls in a smectic-C* phase. If the spacing of these defects is in the subvisible range, this modulated smectic-C* phase would be similar macroscopically to a smectic-A phase. The application of an electric field distorts the array, producing a large polarization, and hence a large electroclinic effect. We show that with suitable elastic parameters and sufficiently large chirality, the modulated phase is favored over the smectic-A and helically twisted smectic-C* phases. We propose various experimental tests of this scenario.

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.

Influence of electric fields on the smectic layer structure of ferroelectric and antiferroelectric liquid crystal devices

The electric-field-induced structural rearrangement of smectic layers in the antiferroelectric and ferroelectric phases of three different materials is reported. The materials all have high optical tilt angles (around 30 degrees ), compared with the steric tilt angles deduced from layer spacing measurements (around 18 degrees ). The chevron angles observed in devices agree well with values found for the steric tilt angle across the tilted mesophase range. Electric fields were applied to liquid crystal devices while the smectic layer structures, in both the depth and in the plane of the device, were probed using small angle x-ray scattering. Two separate aspects of the influence of the field on the layer structure were studied. First, the organization of the smectic layers in the antiferroelectric phase is described before, during, and after the application of an electric field of sufficient magnitude to induce a chevron to bookshelf transition. Second, the evolution of the field-induced layer structure change has been investigated as the field was incrementally increased in both the antiferroelectric and ferroelectric phases. It was found that the chevron to bookshelf transition has a distinct threshold in the antiferroelectric phase, but shows low or zero threshold behavior in the ferroelectric phase for all the materials studied.