Ferroelectric Nematic-Isotropic Liquid Critical End Point.

A critical end point above which an isotropic phase continuously evolves into a polar (ferroelectric) nematic phase with an increasing electric field is found in a ferroelectric nematic liquid crystalline material. The critical end point is approximately 30 K above the zero-field transition temperature from the isotropic to nematic phase and at an electric field of the order of 10 V/µm. Such systems are interesting from the application point of view because a strong birefringence can be induced in a broad temperature range in an optically isotropic phase.

Complex temperature dependence of the dielectric response in simple SmC* phases.

The system under study has a SmA*↔SmC* phase sequence and is described by a basic phenomenological model. However, in contrast to a common approach, changes of the polarisation induced by the external electric field are considered independent of changes of the tilt. As a result, even in the basic model, which does not contain any additional terms usually used to obtain better fits to experimental observations, the frequencies of most of the relaxation modes depend on the temperature non-linearly and their dielectric response is not inversely proportional to the frequency of the mode. The behaviour is a direct consequence of chiral piezoelectric coupling, which influences the polar properties of the relaxation modes depending on the temperature.

Systems with competing interlayer interactions and modulations in one direction: finding their structures.

Complex structures in polar smectic systems can be studied within framework of discrete phenomenological models. Considered interactions are usually described by nonlinear trigonometric functions that do not allow for a straightforward search for solutions. The review of three methods reported in the literature are presented and their appropriateness, advantages and disadvantages are discussed. Examples are given as an illustration for each method.

Chiroclinic effect and the phase diagram of achiral polar molecules in the antiferroelectric smectic B_{2} phase.

The paper presents a detailed analysis of the effects of chiral doping on antiferroelectric B_{2} subphases in bent core systems. The studied system exhibits the phase sequence SmA↔SmAP_{A}↔SmC_{S}P_{A}. The chiral dopant induces the tilt in the SmAP_{A} phase or the tilt modulation in the SmC_{S}P_{A} phase, which is known as the chiroclinic effect, but it also influences the stability ranges and the order of the transition between the phases. The order of the phase transition changes from a continuous for weak effects of chiral doping to discontinuous for strong effects. Competition of interactions results in changes of the phase sequences, which are resumed in the phase diagram. The method that leads to these findings, which could be used for the analysis of other similar systems, is briefly presented as well.

Polar structures in binary mixtures of bent-core liquid crystals showing ferroelectric and antiferroelectric B2 phases.

We have studied the polar structures in the binary mixtures of bent-core liquid crystals P-n-O-PIMB(n-2)*-(n-4)O showing the ferroelectric smectic- CAPF (Sm-CAPF) (n=8 and 10) and antiferroelectric Sm-CSPA (n=9) B2 phase. Although the polar structure of the one-to-one mixture is governed by the compound with longer end chains, it is much more complicated in the mixtures with slightly less fraction of compounds with longer end chains. Even if the mixtures show the antiferroelectric phase before field application, the ferroelectric domains remain once the field is applied and coexist with the antiferroelectric domains. The coexistence structure was modeled by comparing the microscope real image with that of second-harmonic generation. The fraction of the ferroelectric domains is larger at higher temperature region of the B2 phase and decreases with decreasing temperature. The stable phase structures were discussed based on the phenomenological theory. We suggest that the coupling energy of the layer chirality is higher than the energies of the orientation correlations of tilts and polarizations between adjacent layers.

Polar order and tilt in achiral smectic phases.

Material with the phase sequence SmA-SmAP-SmCP is studied as an example of a system in which the spontaneous electric polarization and the molecular tilt develop independently at the SmA-SmAP and the SmAP-SmCP phase transition, respectively. The temperature dependence of the spontaneous electric polarization clearly shows a strong coupling between the polarization and tilt. The system exhibits also very strong precritical polarization and tilt fluctuations. Experimental observations are explained within the theoretical model.

Interpretation of the odd-even behavior for the emergence of ferroelectricity and antiferroelectricity in bent-core mesogens.

Simple theoretical interpretation has been made on the previously reported odd-even behavior of the emergence of ferroelectricity and antiferroelectricity in homologous series of bent-core mesogens with the same chiral end chains (S,S) ; compounds with even and odd carbon numbers (including oxygen) exhibit ferroelectric and antiferroelectric B2 phases, respectively. The odd-even behavior was confirmed in newly synthesized racemic compounds with chiral end chains of R and S forms (R,S) together with (R,R) and (S,S) forms. According to our theoretical interpretation, ferroelectricity should be more stable in (R,S) compounds than in (S,S) compounds. Actually, the transition temperature from the isotropic phase to the Sm-CP phase was higher and the temperature range of the B2 phase was broader in the (R,S) compound than in the (S,S) compound.

Short-range smectic fluctuations and the flexoelectric model of modulated nematic liquid crystals.

We show that the flexoelectric model of chiral and achiral modulated nematics predicts the compression modulus that is by orders of magnitude lower than the measured values. The discrepancy is much larger in the chiral modulated nematic phase, in which the measured value of the compression modulus is of the same order of magnitude as in achiral modulated nematics, even though the heliconical pitch is by an order of magnitude larger. The relaxation of a one-constant approximation in the biaxial elastic model used for chiral modulated nematics does not solve the problem. Therefore, we propose a structural model of the modulated nematic phase, which is consistent with the current experimental evidence and can also explain large compression modulus: the structure consists of short-range smectic clusters with a fourfold symmetry and periodicity of two molecular distances. In chiral systems, chiral interactions lead to a helicoidal structure of such clusters.

Effect of optical purity on phase sequence in antiferroelectric liquid crystals.

We use the discrete phenomenological model to study theoretically the phase diagrams in antiferroelectric liquid crystals (AFLCs) as a function of optical purity and temperature. High sensitivity of the phase sequence in the AFLCs to optical purity is attributed to the piezoelectric coupling which is reduced if optical purity is reduced. We limit our study to three topologically equal smetic (Sm)phases: Sm-C(*), Sm-C(*)(alpha), and Sm-C(*)(A) and show that the reduction of optical purity forces the system from the antiferroelectric to the ferroelectric phase with a possible Sm- C(*)(alpha) between them. The effect of the flexoelectric and the quadratic coupling is considered as well. If the phase diagram includes only two phases, Sm-C* and Sm- C*(A), the flexoelectric coupling is very small. The materials which exhibit the Sm-C(*)(alpha) in a certain range of optical purity and temperature, can be expected to have a significant flexoelectric coupling that is comparable with the piezoelectric coupling. Upon lowering the temperature the phase sequence Sm-A-->Sm-C(*)(alpha)-->Sm-C*-->Sm-C(*)(A) is possible in systems where quadratic coupling is very strong.

Paraelectric-antiferroelectric phase transition in achiral liquid crystals.

Critical freezing of molecular rotation in an achiral smectic phase, which leads to polar ordering through the second order paraelectric-antiferroelectric (Sm-A-->Sm-APA) phase transition is studied theoretically and experimentally. Strong softening of the polar mode in the Sm-A phase and highly intensive dielectric mode in the Sm-APA phase are observed due to weak antiferroelectric interactions in the system. In the Sm-APA phase the dielectric response behaves critically upon biasing by a dc electric field. Such a behavior is found general for the antiferroelectric smectic phase with significant quadrupolar interlayer coupling.

Electric-field-induced transition between the anticlinic and the synclinic smectic-C surfaces in free-standing films.

Anticlinic smectic-C surfaces were found experimentally as ground state structures in free-standing films made of smectic liquid crystals with no anticlinic bulk phases. A mean-field interpretation of this observation is given within a discrete phenomenological model of antiferroelectric liquid crystals, which additionally considers the enhanced order present at the surfaces of the free-standing films. The temperature dependence of the critical electric field that drives the transition between the anticlinic and synclinic smectic-C surfaces is evaluated, and fair agreement with the experimental data is found.

Devil's staircase and harmless staircase in the smectic-C*alpha phase in an electric field.

The unwinding of the short pitch helical smectic-C*alpha structure in an external electric field is studied within a discrete phenomenological model. It is found that the pitch increases quasicontinuously at low electric fields and is commensurate with the smectic layer thickness at any field. The sequence of stable structures recalls the once popular and then abandoned devil's staircase model. At larger fields the pitch grows discontinuously in steps of one smectic layer, forming a harmless staircase. Taking into account the achiral next-nearest-layer interactions the final transition to the unwound structure is found to be discontinuous.

Flexoelectricity in chiral nematic liquid crystals as a driving mechanism for the twist-bend and splay-bend modulated phases.

We present a continuum theoretical model describing the impact of chirality on nematic systems with large flexoelectricity. As opposed to achiral materials, where only one type of the modulated structure can exist in a given material, the model predicts that chirality can stabilize several modulated phases, which have already been observed experimentally [A. Zep et al., J. Mater. Chem. C 1, 46 (2013)].

Reentrant orthogonal smectic-A phase below a tilted smectic-C phase in a chiral compound.

A reentrant orthogonal smectic-A (SmA) phase below the tilted smectic-C phase is established in a chiral liquid crystalline compound. The temperature evolution of the layer spacing confirms monolayer structure in both SmA phases, the upper SmA as well as the reentrant SmA phase. The reentrancy of the SmA phase is explained on the basis of the mean field free energy taking into account nonmonotoneous temperature dependence of the lowest term coefficient.

Ferroelectric behavior of orthogonal smectic phase made of bent-core molecules.

Ferroelectric behavior in the recently reported orthogonal ferroelectric Sm-A(d)P(F) phase in an unsymmetric bent-core molecule with a carbosilane terminal group was studied. The ferroelectricity of the Sm-A(d)P(F) phase was unambiguously confirmed by optical second-harmonic generation activity in the absence of an electric field, ferroelectric response, and high dielectric strength. The long-range polar order is a consequence of weakened interlayer coupling due to the formation of carbosilane sublayers, which allows for the parallel order of dipole moments of bent-core molecules in the neighboring layers. It develops in the system gradually through the second-order phase transition from the orthogonal Sm-A(d) phase. In the Sm-A(d)P(F) phase the strong surface anchoring results in the splay of polarization across the sample thickness. The polar surface anchoring also brings about strongly thickness-dependent polar fluctuations, as proved by the dielectric measurements (Goldstone-like mode). The relaxation frequency and dielectric strength vary more than one order of magnitude with cell thickness; in particular the dielectric strength attains more than 2000 in a 25 µm-thick cell and continues to increase for thicker cells. Simple theory developed qualitatively explains the experimental results, supporting the polarization splay model proposed.

Theoretical analysis of continuous pitch evolution and reversed phase sequence in antiferroelectric liquid crystals.

Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted Sm C(alpha)* phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted Sm C* phase appeared below the four-layer Sm CFI2* phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.

Switching mechanism in polar columnar mesophases made of bent-core molecules.

The behaviour of polar, broken-layer-type columnar phases made of bent molecules (B(1Rev) and B(1RevTilted)) was studied under an applied electric field. There are two competing mechanisms of ferroelectric switching in the polar B(1RevTilted) columnar phase: collective rotation around the long molecular axis and collective rotation around the tilt cone. The proposed model shows that the main factor discriminating the type of switching is the width of the column cross-section.

Spontaneous breaking of minimal surface condition: labyrinths in free standing smectic films.

We present a study of thin free standing films made of intercalated smectic-C liquid crystal in which, upon lowering the temperature, the minimal surface area condition is broken. A periodic modulation of the film thickness is obtained and a labyrinth structure of crests and valleys is formed. Thickness variation is coupled to the spatial variation of the molecular orientation. The transition to the labyrinth structure is explained to be driven by the mass density difference between the surface and the bulk layers.

Ferroelectric mesophase with randomized interlayer structure.

We present the experimental and theoretical evidence that a new Sm X phase made of asymmetric bent-shaped molecules has a layered, nontilted, optically uniaxial and polarly ordered structure with random direction of the layer polarization. The randomness results from the sign degeneracy of the difference in polarization directions in neighboring layers, although the magnitude of the phase difference is constant. Lifting the degeneracy by external fields two additional structures of the Sm X phase are possible.