Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal

Variety of subphase emerging sequences, the frustration of three main phases, SmC_{A}^{*}, SmC^{*}, and SmA, and the long-range interlayer interactions

Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)2470-004510.1103/PhysRevE.96.012701], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of SmC_{A}^{*}, SmC^{*}, and SmA with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of SmC_{α}^{*} which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is SmC_{A}^{*}(SmC_{α}^{*})-1/4-1/3-2/5-3/7-1/2-SmC^{*}(SmC_{α}^{*}), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between SmC_{A}^{*}(SmC_{α}^{*}) and (SmC^{*})SmC_{α}^{*}. Moreover, the experimentally confirmed extraordinary subphase emerging sequence SmC^{*}-1/2-SmC_{α}^{*} appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from SmC_{A}^{*} and SmC^{*} to SmC_{α}^{*} is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence SmC_{A}^{*}-1/3-SmC^{*} does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.

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 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.

Superlattice structures observed in the extraordinary phase sequence and analyzed by the phenomenological Landau model and the partially molecular model

We draw several electric-field-temperature (E-T) phase diagrams with electric-field-induced birefringence contours in the nOHFBBB1M7 (n=10) and nOTBBB1M7 (n=11) (C11) mixture system by changing the C11 concentration carefully; some of the mixtures show the unusual extraordinary phase sequence where subphases with the four-, five-, and six-layer superlattice structures emerge above the smectic-C(*) main phase. We try to understand the results in terms of two complementary models that have so far been proposed: the phenomenological Landau model of phase transitions by Dolganov et al. [P. V. Dolganov et al., Phys. Rev. E 86, 020701(R) (2012)] and the partially molecular Emelyanenko-Osipov model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)]. The observed E-T phase diagram can be well reproduced by the phenomenological model. An emergence of the subphase with the four-layer superlattice structure above smectic-C(*) is also understandable in terms of the partially molecular model. We discuss the pros and cons of the two models as well.

Commensurate polar smectic structures with a two-component order parameter

Recently Wang [Phys. Rev. Lett. 104, 027801 (2010)] discovered a novel smectic-C* liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.

Discovery of a novel smectic-C{*} liquid-crystal phase with six-layer periodicity

We report the discovery of a new smectic-C{*} liquid-crystal phase with six-layer periodicity by resonant x-ray diffraction. Upon cooling, the new phase appears between the SmC{alpha}{*} phase having a helical structure and the SmC{d4}{*} phase with four-layer periodicity. This SmC{d6}{*} phase was identified in two mixtures which have an unusual reversed SmC{d4}{*}-SmC{*} phase sequence. The SmC{d6}{*} phase shows a distorted clock structure. Three theoretical models have predicted the existence of a six-layer phase. However, our experimental findings are not consistent with the theories.

Recovery of a reversed phase sequence in one ternary liquid-crystal-mixture system

The nOHFBBB1M7 (n=10) compound, 10OHF, shows a reversed SmC{FI2}-SmC phase sequence, unique among all known antiferroelectric liquid crystals. This reversed phase sequence is stabilized when 10OHF is doped with 9OTBBB1M7(C9) or 11OTBBB1M7(C11). In contrast, doping of the homologous members ( n=9 , 11, or 12) eliminates the SmC{FI2} phase. One 10OHF/11OHF mixture without the SmC{FI2} phase was selected for further studies. By adding C9 into this particular mixture, the reversed phase sequence is revived. To our surprise, even though 11OHF destabilizes the SmC_{FI2} phase in binary mixtures with 10OHF, it significantly increases the SmC_{FI2} temperature range in the 10OHF/11OHF/C9 ternary mixtures.

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.

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.

Unique pitch evolution in the smectic-C+alpha phase

Employing resonant x-ray diffraction, we observed unique pitch evolutions in the smectic-C*(alpha) phase in mixtures of two antiferroelectric liquid crystals. Our results show that the pitch in this phase continuously evolves across 4 layers, contradicting a theoretical model that predicts that the smectic-C*(FI2) phase intervenes in the smectic-C*(alpha) phase. The phase sequences we found can be explained by another model that includes one type of long-range interaction among smectic layers.

Range of interlayer interactions in smectic- C liquid crystals

The fact that the elastic constant for bending a layer of smectic- C liquid crystal along its c director differs from the value for bending in the perpendicular direction has recently been shown to give rise to interactions between distant layers. The effect of this entropy-induced interaction is to favor a parallel or antiparallel alignment of the c directors in these nonadjacent layers. We calculate in detail the range and strength of this interaction in both infinite and finite samples, and find the results to depend mainly on the ratio of the average layer bending elastic constant to the layer compression modulus. At low values of this ratio, the interlayer interaction is of long range in a bulk sample, while at high values of the ratio it decays as the inverse cube of the interlayer distance. For a sample confined between rigid substrates parallel to the layers, the interaction is greatly reduced. For a free-standing film the interaction may be enhanced if the surface tension is weak, but may be diminished if the surface tension is strong.