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

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.

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.

Degeneracy lifting due to thermal fluctuations around the frustration point between anticlinic antiferroelectric SmC(A)* and synclinic ferroelectric SmC*

In the binary mixture phase diagram of MC881 and MC452, the borderline between anticlinic antiferroelectric SmC(A)(*) and synclinic ferroelectric SmC(*) becomes apparently parallel to the temperature ordinate axis at the critical concentration r(c). The free energy difference between SmC(A)(*) and SmC^{*} is extremely small in a wide temperature range near r(c). In such circumstances, by observing Bragg reflection spectra due to the director helical structure and electric-field-induced birefringence, we have observed the continuous change from SmC(A)(*) to SmC(*) for r</~r(c) and the gradual growth of the full-pitch band over 5 °C or more in the apparent SmC(*) temperature region for r>/~r(c). These intriguing phenomena have been explained, successfully at least in the high-temperature region, by a thermal equilibrium between the synclinic and anticlinic orderings and the resulting Boltzmann distribution for the ratio between them; the thermal equilibrium is considered to be attained in a nonuniform defect-assisted way through solitary waves moving around dynamically. We have also discussed qualitatively an important role played by the effective long-range interlayer interactions in the low-temperature region.

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.