Field-induced transitions between multilayer phases of polar smectic liquid crystals

Molecular origin of the heterogeneity in the nematic and smectic liquid crystals: Elastic constants, gradients of order parameters, and visualization of small objects

The formation of heterogeneous nematic and smectic liquid crystals in the general case of an arbitrary geometry is investigated in the framework of molecular-statistical approach [Emelyanenko and Khokhlov, J. Chem. Phys. 142, 204905 (2015)JCPSA60021-960610.1063/1.4921684]. The molecular aspects of the orientational and translational orderings at the curved surfaces of small solid objects dispersed in liquid crystal are considered, and the differential equations for gradients of the order parameters in vicinities of the small objects are presented in the general form. The five elastic constants are obtained within the same approach, from which we were able to predict that a significant space variations of the order parameters can be observed within the 0.5-0.8μm area around any small object, almost independently of its own dimension. Therefore, the liquid crystals can be a simple tool for the optical visualization of nano-objects. It is also demonstrated that the kind of molecular self-organization (smectic, nematic or conventionally isotropic) at the surfaces of small solid objects can be different from that in the bulk of mesogenic material. Totally we predict eight various combinations of simple states at the surfaces and in the bulk depending on the solid objects' size and temperature. It is also shown that the surfaces of 10μm-size solid objects and larger act almost as flat surfaces, while the surfaces of 1μm-size solid objects and smaller act almost as point defects.

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.

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.

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.

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.

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.