Unique pitch evolution in the smectic-C+alpha phase

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.

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.

Chiral heliconical ground state of nanoscale pitch in a nematic liquid crystal of achiral molecular dimers

Freeze-fracture transmission electron microscopy study of the nanoscale structure of the so-called "twist-bend" nematic phase of the cyanobiphenyl (CB) dimer molecule CB(CH2)7CB reveals stripe-textured fracture planes that indicate fluid layers periodically arrayed in the bulk with a spacing of d ~ 8.3 nm. Fluidity and a rigorously maintained spacing result in long-range-ordered 3D focal conic domains. Absence of a lamellar X-ray reflection at wavevector q ~ 2π/d or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic rather than smectic molecular ordering. A search for periodic ordering with d ~ in CB(CH2)7CB using atomistic molecular dynamic computer simulation yields an equilibrium heliconical ground state, exhibiting nematic twist and bend, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer. We measure the director cone angle to be θ(TB) ~ 25° and the full pitch of the director helix to be p(TB) ~ 8.3 nm, a very small value indicating the strong coupling of molecular bend to director bend.

Effect of intralayer inhomogeneity on helical superstructures of liquid crystals

A mechanism to form distorted helical structures in ferroelectric liquid crystals is presented. It is shown that the deformation of helical interlayer structures of thin smectic systems can be considered as a direct consequence of the surface-induced spatial inhomogeneity in the distribution of the azimuthal molecular orientation within smectic layers. The intralayer azimuthal nonuniformity occurring in helical phases is argued to generate a local depolarizing electric field of the strength varying not only in smectic layers but also between the layers. The resulting modulation of the depolarization level in the direction of helical axes is shown to lead to a distortion of helices. Using a simple model, including the depolarization interaction, it is demonstrated that the degree of the helix deformation strongly varies as parameters of the model are changed. It is also shown that strong deformations of extremely short helices, found for appropriate values of the parameters, reflect nonuniformity of helicoidal superstructures of respective smectic subphases in real liquid crystalline systems.

Manifold of polar smectic liquid crystals with spatial modulation of the order parameter

We revisit a theoretical approach based on the discrete Landau model of polar smectic liquid crystals. Treating equilibrium structures on many length scales, we have analyzed different periodically modulated polar smectic phases. Besides already known smectic structures, we have obtained a number of other phases which are stable in a narrow range (that is why the phases can be termed as microphases) of model parameters and thermodynamic conditions. The sequence of microphases represents a so-called "harmless staircase" of structures with oscillating periods. We anticipate that the range of stabilities for various microphases can be extended (and therefore the microphases can be easier to detect experimentally) by applying external electric fields or/and investigating freestanding smectic films.

Continuum theory of tilted chiral smectic phases

We show that the sequence of distorted commensurate phases observed in tilted chiral smectics is explained by the gain in electrostatic and elastic energies due to the lock-in of the unit cell to a number of layers which is the integer closest to the ratio of the helix pitch over the smectic layer thickness of the subjacent Sm-Cα∗ phase. We also explain the sign change of the helicity in the middle of the sequence by a balance between two twist sources one intrinsic and another due to the distortion of the Sm-Cα∗.

Theoretical analysis of continuous pitch evolution and reversed phase sequence in antiferroelectric liquid crystals

Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted Sm C(alpha)* phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted Sm C* phase appeared below the four-layer Sm CFI2* phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.

Behavior of the helix in some chiral smectic-C* liquid crystals

In spite of numerous papers dedicated to the subject, the behavior of the helical pitch in the smectic C* phase near the smectic A phase is still controversial. In particular, it is not clear to what extent the measured pitch values are influenced by surface effects. In order to shed light on this problem, careful pitch measurements have been performed using different methods and sample preparations. We have found that the diffraction of light on planar-oriented samples may give incorrect pitch results because of strong influence of the surfaces and possibly of the sample texture on the helical structure. We have demonstrated that using appropriate preparation of samples the bulk properties of the helix can be determined. It has been found that a maximum of pitch can indeed occur but then only when very close to the transition point smectic C*-->smectic A (about 0.1 K). The results of helical pitch measurements have been compared with predictions of theories.

Extension of the Hamaneh-Taylor model using the macroscopic polarization for the description of chiral smectic liquid crystals

Chiral smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate Sm-Calpha* phase. We carried out an extension of the phenomenological model recently presented by Hamaneh and Taylor based on the distorted-clock model. The salient feature of this model is that it links the appearance of phases to a spontaneous microscopic twist: i.e., an increment alpha of the azimuthal angle from layer to layer. The balance between this twist and an orientational order parameter J gives the effective phase. We introduce a second orientational order parameter I , which physical meaning comes from the macroscopic polarization; the effect of an applied electric is also studied. We derive phase diagrams and correlate them to our experimental results under field showing the sequence of phases versus temperature and electric field in some compounds.

Experimental study of high-temperature smectic- C_{FI2}{ *} phase in chiral smectic liquid crystals that exhibit phase-sequence reversal

We report the results of an experimental study of a recently observed phase sequence reversal of smectic-C_{FI2}{ *} [ SmC;{ *}(q_{T}=1/2); a four layer antiferroelectric] phase appearing in the temperature range above the smectic-C{ *} (SmC;{ *}) phase from the results of optical birefringence, spontaneous polarization, selective reflection, conoscopy, and dielectric spectroscopy. The SmC_{FI2}{ *} phase is observed in an antiferroelectric liquid crystalline compound, 10OHF, in a temperature range above that of SmC{ *} phase and is found to be thermodynamically monotropic, i.e., it appears only upon cooling from SmC_{alpha}{ *} phase. This is also unstable as if it is once transformed to SmC{ *} by the application of the bias, it does not return to its original state unless the sample is heated and cooled again in the absence of the bias. Nevertheless this phase is stabilized by the addition of a chiral smectic compound 9OTBBB1M7 (abbreviated as C9), having a wide temperature range of the SmC_{FI2}{ *} phase. The temperature range of the low temperature SmC{ *} decreases with increase in the concentration of C9 and for a concentration of 55 wt. %, SmC{ *} disappears and the transition takes place directly from SmC_{FI2}{ *} to the crystalline phase on cooling. The existence of such a high-temperature SmC_{FI2}{ *} phase is also supported by a phenomenological model.

Characteristics of the collective dielectric relaxation mode of the incommensurate SmC(α)(*) phase

Employing the dielectric relaxation spectroscopy technique, we have observed two different characteristics of the collective relaxation mode of an incommensurate SmC(α)(*) phase. Recent theoretical advances predict two different natures for the dielectric relaxation mode in the SmC(α)(*) phase. Our experimental results confirm two different behaviours of the relaxation mode in different temperature ranges for this phase for one unique compound having an exceptionally wide temperature range (∼9 °C) for the SmC(α)(*) phase.