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

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.

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.

Effective long-range interlayer interactions and electric-field-induced subphases in ferrielectric liquid crystals

Microbeam resonant x-ray scattering experiments recently revealed the sequential emergence of electric-field-induced subphases (stable states) with exceptionally large unit cells consisting of 12 and 15 smectic layers. We explain the emergence of the field-induced subphases by the quasimolecular model based on the Emelyanenko-Osipov long-range interlayer interactions (LRILIs) together with our primitive way of understanding the frustration in clinicity using the q_{E} number defined as q_{E}=|[R]-[L]|/([R]+[L]); here [R] and [L] refer to the numbers of smectic layers with directors tilted to the right and to the left, respectively, in the unit cell of a field-induced subphase. We show that the model actually stabilizes the field-induced subphases with characteristic composite unit cells consisting of several blocks, each of which is originally a ferrielectric three-layer unit cell stabilized by the LRILIs, but some of which would be modified to become ferroelectric by an applied electric field. In a similar line of thought, we also try to understand the puzzling electric-field-induced birefringence data in terms of the LRILIs.

Anisotropy of electrostatic interaction in smectic-C^{*} liquid crystals

The contribution to the free energy of distortion of the ferroelectric smectic-C^{*} due to the electrostatic interaction of polarization charges is calculated. These calculations are performed by accounting for the anisotropy of the permittivity, which is essential for smectic-C^{*}. Fluctuations of the c director in an external electric field are considered. It is shown that the anisotropy of the permittivity strongly affects the interaction of the polarization charges, the spectrum orientation fluctuations, and the angular dependence of the light scattering intensity.

Resonant x-ray diffraction spectrum for possible structures of the smectic liquid crystal phase with a six-layer periodicity

With the discovery of the smectic-C(d6)(*) (SmC(d6)(*)) phase showing six-layer periodicity [S. Wang et al., Phys. Rev. Lett. 104, 027801 (2010)] and a recent report of the observation of a possible alternative structure, the need for a reliable and accurate method for distinguishing different possible structures is more urgent than ever. Through simulations using the tensorial structure factor method, we present the resonant x-ray diffraction (RXRD) spectra for different possible structures as proposed in several theoretical studies. Subtle distinctions between models are shown. The ability and limitations of RXRD as a technique for determining the structure of this particular phase is discussed.

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.

Effect of an external electric field on the smectic-Ctilted* phases

We are interested in the chiral tilted smectic subphases, smectic-C(tilted)(*), including commensurate structures as well as the incommensurate smectic-C(α)(*) one. The continuum theory defines two scalar order parameters I and J, which can be coupled with an external electric field through a linear term I × E and a dielectric term J × E(2). We have calculated the changes due to these terms in the phase diagrams in the (α,η) plane, where α comes from the spontaneous twist and η measures the strength of the biaxial order. The coupling with an external electric field induces the expansion of the areas with spontaneous polarization and the appearance of an electroazimuthal effect.