Field-induced phase transitions in antiferroelectric liquid crystals

Response to an applied electric field in an antiferroelectric 1/2 subphase: The role of thermal fluctuations

The response to an applied electric field in the q_{T}=1/2 subphase of the MC881-MC452 binary mixture system is studied by using thick homeotropically aligned cells. In the ordinary antiferroelectric SmC_{A}^{*} and 1/2 (sub)phases, some nonplanar asymmetric distortions in the antiferroelectric unit cell structure produce induced polarization in the applied field direction, starts to unwind the helix from the beginning, and tends to align the averaged tilt plane direction parallel to the applied field. In the 1/2 subphase under consideration, however, the helix resists being deformed at the beginning and then the thresholdlike steep increase of birefringence Δn occurs in the transition from 1/2 to unwound SmC^{*} at a field of less than 0.5 V/µm; we conclude that the thermal fluctuations play an important role in promoting the director flip-flopping in a single layer under the applied field and bring about additional induced polarization, which counteracts the aforementioned ordinary induced one and prevents the helix from unwinding. This suggests that the Langevin-like director reorientation is the mechanism of the V-shaped switching which was actually observed in the thin films of Mitsui mixture [Phys. Rev. Lett. 87, 015701 (2001)0031-900710.1103/PhysRevLett.87.015701] and must have been used in prototyped thresholdless antiferroelectric liquid-crystal displays.

Dielectric study of a subphase stabilized in an exceptionally wide temperature range by a delicate balance of interlayer interactions and thermal fluctuations

The chiral smectic phases of calamitic liquid crystals, SmC^{*} and SmC_{A}^{*}, are characterized by the synclinic ferroelectric F ordering and the anticlinic antiferroelectric A ordering in adjacent layers. Various states with mixed A and F orderings are degenerate at the frustrated phase-transition point. The degeneracy lifting is commonly caused by the long-range interlayer interactions (LRILIs), producing a series of biaxial subphases specified by a relative ratio of both orderings, q_{T}=[F]/([A]+[F]). Sandhya et al. [Phys. Rev. E 87, 012502 (2013)PLEEE81539-375510.1103/PhysRevE.87.012502] established, however, the importance of thermal fluctuations in the degeneracy lifting in some binary mixtures of MC881 and MC452. They observed the most intriguing interplay of thermal fluctuations and LRILIs in the stabilization of an apparently single subphase. Since no other detailed experimental study of the subphase has so far been made, we carry out its dielectric investigations and clarify the following five points: (1) the subphase is surely a single phase from ≈80^{∘}C down to room temperature; (2) the imaginary part of complex permittivity ε^{″} shows the weak antiphase mode and hence it must be antiferroelectric q_{T}=1/2; (3) ε^{″} becomes much stronger above ≈80^{∘}C, indicating the emergence of ferroelectric and/or ferrielectric states; (4) the dielectric amplitude gradually increases at least just above the 1/2 subphase, suggesting it be due to a continuous increase of q_{T}; and (5) at low temperatures the antiphase relaxation mode shows irregularities that indicate the important role played by the cooperative motion of the layer undulation as well as of the director tilting.

Unexpected electric-field-induced antiferroelectric liquid crystal phase in the SmC_{α}^{*} temperature range and the discrete flexoelectric effect

The unique nanometer-sized helical structure in SmC_{α}^{*} may sometimes evolve continuously to the micrometer-sized one in SmC^{*}; conceivably ferroelectric SmC_{α}^{*} is to be unwound by an applied electric field. By drawing electric-field-induced birefringence contours in the field-temperature phase diagram and by studying the superlattice structure of the field-induced subphase with resonant x-ray scattering, we established that an applied field unexpectedly stabilizes the well-known antiferroelectric four-layer biaxial subphase as well as the other prototypal ferrielectric three-layer one in the SmC_{α}^{*} temperature range; the effective long-range interlayer interaction due to the discrete flexoelectric effect actually plays an important role in stabilizing not only the biaxial subphases but also the optically uniaxial SmC_{α}^{*} subphase, contrary to the notion that the competition between the direct interactions of the nearest-neighbor layers and those of the next-nearest-neighbor layers should be required for the nanometer-sized helical structure.

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].

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.

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.

Theory for the evolution of ferroelectric, antiferroelectric, and ferrielectric smectic phases in the electric field

An evolution of Sm-C(A)∗, biaxial intermediate phases, and Sm-C∗ in the electric field is investigated in a framework of molecular-statistical approach [A. V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006); A. V. Emelyanenko, Eur. Phys. J. E 28, 441 (2009)]. The "electric field-temperature" phase diagrams including the possibility of existence of various tilted smectic phases are plotted and compared with the experimental ones. Permanent transverse molecular dipole moments (without electric field participating only in the spontaneous polarization) were also found to generate the induced polarization in the presence of electric field and to produce very strong dielectriclike effect. This effect is positive in Sm-C∗ (tilt planes have a tendency of orienting along or against the electric field) and is negative in Sm-C(A)∗ and in biaxial intermediate phases (tilt planes have a tendency of orienting perpendicular to the electric field). In the ferrielectric intermediate phases both spontaneous and induced polarizations favor similar tendencies and provide the helix unwinding at very low electric field. At the same time, the tendencies provided by spontaneous and induced polarizations are opposite in Sm-C∗, and therefore the unwinding threshold is larger. It was shown that interplay between spontaneous and induced polarizations can lead to the formation of complex bidomain smectic structures. A single parameter regulating an evolution of structure of Sm-C∗, Sm-C(A)∗, and biaxial intermediate phases in the electric field was found. We suppose that bidomain helical structure is the same as additional ferrielectric phase FiLC existing in some materials just below Sm-C∗. The numerical calculations are done with help of AFLC phase diagram plotter software developed by the author and available at his webpage.

Unwinding of the antiferroelectric helix in an electric field

Using the discrete phenomenological model with interlayer anticlinic and chiral interaction, the unwinding of the antiferroelectric helix in external electric field was studied. The dependence of the helical pitch on the electric field differs essentially in antiferroelectric and ferroelectric phases. It was found that in antiferroelectric the critical electric field E h of the transition into the unwound structure is proportional to the value of chiral interaction and does not depend on the anticlinic interaction between nearest layers. This behavior differs significantly from the case of ferroelectric in which E h increases as the square of the chiral interaction and is inversely related to the synclinic interaction between layers. Peculiarities of the unwinding process and the dependence of the critical field E h on model parameters are discussed. Based on our calculations, we propose an analytical equation for the critical unwinding field in the antiferroelectric.

Molecular-statistical approach to a behavior of ferroelectric, antiferroelectric and ferrielectric smectic phases in the electric field

The fundamental theoretical approach derived in A.V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006) is complemented by a consideration of the influence of the homogeneous electric field on Sm-CA*, biaxial intermediate phases, and Sm-C*. The crucial role of the induced polarization is investigated for the first time. The evolution of any tilted smectic phase in the electric field is found to meet the two thresholds. The first threshold corresponds to the unwinding process, and the second one corresponds to the phase transition into the bi-domain structure of Sm-C*, where the tilt plane has some contribution either along or against the electric field, while the average direction may still be perpendicular to the electric field. The tilt plane in the monodomain (conventional) structure preceding the second threshold is the same in every unwound phase, and is perpendicular to the electric field. No 3D distortion in Sm-CA* is predicted on application of the electric field. The entire electric-field-temperature phase diagrams including the possibility of existence of the maximal number of tilted smectic phases are plotted and compared with the experimental ones. The numerical calculations in the framework of this fundamental study are done with help of AFLC Phase Diagram Plotter software developed by the author and available at his web page.

Gradual phase transition between the smectic- C and smectic- C{A} phases and the thresholdless antiferroelectricity

We have constructed the phase diagrams for a binary-mixture system of antiferroelectric and ferroelectric liquid-crystalline materials in both thick and thin cells. In the phase diagrams the boundary between the smectic- C and smectic- C{A} phases runs almost parallel to the temperature axis below from ca. 70 degrees C down to at least -25 degrees C . The SmC-SmC_{A} phase transition for a thin cell shows a large supercooling, and a gradual transition occurs near the boundary. Moreover, the thin cell shows a continuous evolution from the antiferroelectric to the ferroelectric state by increasing the electric field applied across the cell. The continuous evolution seemingly reflects the phenomenon of thresholdless antiferroelectricity. In order to explain these phenomena and in clarifying the mechanism of the so-called frustration between ferroelectricity and antiferroelectricity, we have measured the interlayer interaction energy by varying the constituent concentrations in the binary-mixture system. The measured interlayer interaction close to the boundary indicates that the gradual phase transition and continuous evolution result from the suppression of the solitary-wave propagation by the effect of surfaces.

Dynamic mechanism of the ferroelectric to antiferroelectric phase transition in chiral smectic liquid crystals

The temperature-induced phase transition between the chiral smectic phases, antiferroelectric (smectic-C(A)*) and ferroelectric (smectic-C*), is found to occur through solitary wave propagation. We measure the free energy, which shows a double well shape in the entire SmC(A)* temperature range and the global minimum is found to shift from the antiferroelectric order to the ferroelectric order at the transition temperature. However, any significant supercooling is not observed and the transition cannot be described by the first order Landau-de Gennes theory, where the double well potential exists only in a narrow range of temperatures. This implies that the SmC(A)*-SmC* transition can occur only nonhomogeneously through the solitary wave propagation which overcomes the high energy barrier between the two minima.

Field-induced structures and transitions in chiral antiferroelectric liquid crystals

The transformation of a chiral antiferroelectric liquid crystal in an electric field was calculated. Minimization of the free energy was performed with respect to both the phase and the modulus of the two-component order parameter. Competition between the electric field, which favors a planar structure, and chirality and the anticlinic ordering leads to frustration and sequential formation of a distorted helix, a soliton state, transition to an unwound distorted antiferroelectric, and finally the planar synclinic state. In the soliton and distorted antiferroelectric states an anomalous electroclinic effect (the decrease of the tilt angle and layer polarization) was found. The antiferroelectric soliton can be removed by a large electric field only via the transition to the synclinic state.

Solitary wave propagation in antiferroelectric liquid crystal cells and the quadrupolar term in the interlayer interaction

Planar antiferroelectric liquid crystal (AFLC) cells exhibit propagating solitary waves. By measuring the retardation and the apparent tilt angle, we find that the conventional model for the solitary wave propagation in AFLCs is not generally applicable. The model being proposed here shows that the solitary wave propagation both along and normal to the smectic layer plane can be explained by a double well potential energy governing the relative orientations of the c directors in the adjacent smectic C layers with an energy barrier between the synclinic and the anticlinic states. The quadrupolar term of the interlayer interaction is found to be significantly large in a pure AFLC.

Dynamics of electro-optical switching in the antiferroelectric B2 phase of an achiral bent-core shape compound

A detailed study of the dynamics of electro-optical response has been carried out over the whole temperature range of the antiferroelectric B2 phase of a compound with bent-core shape molecules, a homolog (n=14) of the series 4-chloro-1,3-phenylene bis[4-(4-n-alkylphenylimino)benzoates]. Two types of stripe domains were observed with opposite handedness and simultaneous clock and anticlock motion of the director in the neighboring domains. The temperature dependence of the interlayer potential has been found from the threshold of the transition from the ground antiferroelectric (AF) state to the field-induced ferroelectric (F) state. The rotational viscosity gamma(phi) has been calculated from the dynamics of the field-induced azimuthal director switching between F-F and AF-F states and free relaxation of the director from F to AF state. The electro-optical response was also observed below the AF-F threshold. The latter was attributed to the soft-mode distortion of the molecular tilt angle in the vicinity of the transition from the B2 phase to the isotropic phase.

Tilt plane orientation in antiferroelectric liquid crystal cells and the origin of the pretransitional effect

The optic, electro-optic, and dielectric properties of antiferroelectric liquid crystals (AFLCs) are analyzed and discussed in terms of the local tilt plane orientation. We show that the so-called pretransitional effect is a combination of two different electro-optic modes: the field-induced antiphase distortion of the antiferroelectric structure and the field-induced reorientation of the tilt plane. In the presence of a helix, the latter corresponds to a field-induced distortion of the helix. Both electro-optic modes are active only when the electric field has a component along the tilt plane. Thus, by assuring a horizontal surface-stabilized condition, where the helix is unwound by surface action and the tilt plane is everywhere parallel to the cell plates, the pretransitional effect should be suppressed. We also discuss the dielectrically active modes in AFLCs and under which circumstances they contribute to the measured dielectric permittivity.

Orientational distributions in smectic liquid crystals showing V-shaped switching investigated by polarized Raman scattering

Molecular orientational order parameters have been obtained by Raman scattering in two types of liquid crystal materials showing the V-shaped switching in thin homogeneous cells. One is the Mitsui mixture and the other is one component of the Inui mixture. The antiferroelectric phase exists in the bulk of both materials but, in thin homogeneous cells, the stability is distinct from each other. The obtained distribution of the local in-plane directors at the tip of the V is considerably broad in the former, while it is narrow in the latter. These differences have been explained by the barrier between the ferroelectric and antiferroelectric orderings, the chiral twisting power, and the interface induced destruction of the antiferroelectric ordering.

Probable Langevin-like director reorientation in an interface-induced disordered SmC*-like state of liquid crystals characterized by frustration between ferro- and antiferroelectricity

To clarify the thresholdless, hysteresis free V-shaped switching due to frustration between ferro- and antiferroelectricity, we have studied a prototype binary mixture system. The apparent orientational order parameters, <P2> and <P4>, obtained from polarized Raman scattering in thin homogeneous cells indicate that substrate interfaces induce some randomization of local in-plane directors at the tip of the V. Their correlation lengths, xi( parallel) approximately 3.5 nm and xi( perpendicular) approximately 75 nm, have been estimated by assuming the Langevin-like reorientation. Because of the much shorter xi(parallel) and xi(perpendicular) than the visible light wavelength, the switching process looks uniform.

Freedericksz transition in an anticlinic liquid crystal

The Freedericksz geometry is used to show experimentally that a very-long-pitch, surface stabilized, anticlinic liquid crystal undergoes a two-step electric-field-induced transition to the synclinic phase. The liquid crystal remains undistorted below the threshold field E(th). For E>E(th), a Freedericksz transition occurs, wherein molecules in adjacent smectic layers undergo unequal azimuthal rotations about the layer normal, resulting in a nonzero polarization that couples to the applied field. Measurements of E(th) as a function of temperature are reported. Related quasielastic light scattering measurements demonstrate that acoustic Goldstone mode fluctuations are quenched by a dc electric field E>E(th). At high fields a transition to the synclinic phase occurs via solitary waves.

Freedericksz transition in an anticlinic liquid crystal

It is shown experimentally that a very-long-pitch, surface-stabilized, anticlinic liquid crystal undergoes a two-step electric-field-induced transition to the synclinic phase. The liquid crystal remains undistorted below a threshold field E(th). For E>E(th), a Freedericksz transition occurs, wherein molecules in adjacent smectic layers undergo unequal azimuthal rotations about the layer normal. At higher fields a transition to the synclinic phase occurs via solitary waves.