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.

Unmasking the structure of a chiral cubic thermotropic liquid crystal phase by a combination of soft and tender resonant X-ray scattering.

A resonant X-ray scattering response for two structural models of a chiral cubic phase with a giant unit cell, one composed of a continuous grid and micelles and the other with three continuous grids, is studied theoretically and compared to experimental measurements. For both structural models resonant enhancement of all the symmetry-allowed diffraction peaks is predicted, as well as the existance of several symmetry forbidden peaks (pure resonant peaks). Experimental measurements were performed at the carbon and sulphur absorption edge. Only one pure resonant peak was observed, which is predicted by both models. Two low-angle symmetry allowed peaks, not observed in non-resonant scattering, were resonantly enhanced and their intensity angular dependence can distinguish between the two structural models.

Molecular Packing in Double Gyroid Cubic Phases Revealed via Resonant Soft X-Ray Scattering.

The bicontinuous double gyroid phase is one of the nature's most symmetric and complex structures, the electron density map of which was established long ago. By utilizing small-angle x-ray scattering, resonant soft x-ray scattering at the carbon K edge and model-dependent tensor-based scattering theory, we have not only elucidated morphology but also identified molecular packing in the double gyroid phases formed by molecules with different shapes, i.e., rodlike vs taper shaped, thus validating some of the hypothetical packing models and disproving others. The spatial variation of molecular orientation through the channel junctions in the double gyroid phase can be either continuous in the case of anisotropic channels or discontinuous in the case of isotropic channels depending on the molecular structure and shape.

Bi-continuous orthorhombic soft matter phase made of polycatenar molecules.

We report an observation of a new type of a continuous soft matter phase with an orthorhombic symmetry made of polycatenar molecules. The bi-continuous orthorhombic structure with the Pcab symmetry appears by deformation of a double gyroid cubic structure with the Ia3[combining macron]d symmetry.

New structural model of a chiral cubic liquid crystalline phase.

We have studied properties of novel thermotropic mesogenic materials that exhibit both an achiral double gyroid (Ia3[combining macron]d symmetry) and chiral cubic phase (previously assigned the Im3[combining macron]m symmetry). We argue that in the chiral cubic phase molecules form micelles and channels arranged into continuously interconnected hexagons. From the X-ray diffraction experiment supported by modelling, exact positions of hexagons and their connections were deduced and showed to be embedded on a WP (degenerated Neovius) minimal primitive surface. The elastic energy of such a structure is close to the one of the double gyroid phase, which is in agreement with a very low enthalpy change observed at the phase transition. We also argue that the chirality of the phase is related to the lack of mirror symmetry of non-flat hexagons accompanied by an alternating inclination of molecules in the neighbouring segments of hexagon; the chirality of individual hexagon is amplified on the whole hexagon network by steric effects.

Polarization Gratings Spontaneously Formed from a Helical Twist-Bend Nematic Phase.

Spontaneous formation of polarization gratings by liquid crystalline phase made of bent dimeric molecules is reported. The grating is formed within the temperature range of the twist bend modulated nematic phase, NTB , without the necessity to pattern the cell surfaces, therefore the modulated nematic phase is a promising candidate for low-cost modulators and beam steering devices, the polarization properties of which depend on temperature. In addition, the study of the diffracted light properties turns out to be a sensitive measuring technique for determination of the 3D spatial variation of the optic axis in the cell.

Structure of nanoscale-pitch helical phases: blue phase and twist-bend nematic phase resolved by resonant soft X-ray scattering.

Periodic structures of phases with orientational order of molecules but homogenous electron density distribution: a short pitch cholesteric phase, blue phase and twist-bend nematic phase, were probed by resonant soft X-ray scattering (RSoXS) at the carbon K-edge. The theoretical model shows that in the case of a simple heliconical nematic structure, two resonant signals corresponding to the full and half pitch band should be present, while only the full pitch band is observed experimentally. This suggests that the twist-bend nematic phase has a complex structure with a double-helix built of two interlocked, shifted helices. We confirm that the helical pitch in the twist-bend nematic phase is in a 10 nm range for both the chiral and achiral materials. We also show that the symmetry of the blue phase can be unambiguously determined through a resonant enhancement of the X-ray diffraction signals, by including polarization effects, which are found to be an important indicator in phase structure determination.

From Sponges to Nanotubes: A Change of Nanocrystal Morphology for Acute-Angle Bent-Core Molecules.

The crystalline (B4 ) phase made of acute-angle bent-core molecules (1,7-naphthalene derivatives), which exhibits an unusual, highly porous sponge-like morphology, is presented. However, if grown in the presence of low-weight mesogenic molecules, the same crystal forms nanotubes with a very high aspect ratio. The nanotubes become unstable upon increasing the amount of dopant molecules, and the sponge-like morphology reappears. The phase is optically active, and the optical activity is an order of magnitude smaller than in the B4 phase made of conventional bent-core molecules. The optical activity is related to the spatial inhomogeneity of the layered structure and is reduced due to the low apex angle and low tilt of the molecules. The arrangement of molecules within the layers was deduced from the bathochromic absorption shift in the B4 phase.

Monolayer Filaments versus Multilayer Stacking of Bent-Core Molecules.

Bent-core materials exhibiting lamellar crystals (B4 phase), when dissolved in organic solvents, formed gels with helical ribbons made of molecular monolayers and bilayers, whereas strongly deformed stacks of 5-6 layers were found in the bulk samples. The width and pitch of the helical filaments were governed by molecular length; they both increased with terminal-chain elongation. It was also found that bulk samples were optically active, in contrast to the corresponding gels, which lacked optical activity. The optical activity of samples originated from the internal structure of the crystal layers rather than from the helicity of the filaments. A theoretical model predicts a strong increase in optical activity as the number of layers in the stack increases and its saturation for few layers, thus explaining the smaller optical activity for gels than for bulk samples. A strong increase and redshift in fluorescence was detected in gels as compared to the sol state.

Thermal diffusivity anisotropy measured by a temperature wave method in the homologous series of (p-alkoxybenzylidene)-p'-octylaniline (nO.8).

The anisotropy of thermal diffusivity in four homologues of (p-alkoxybenzylidene)-p'-octylaniline (nO.8, n = 4 - 7) was measured using a temperature wave method. The results show that the thermal diffusivity component along the director (α(∥)) is considerably larger than that perpendicular to the director (α(⊥)) in all mesophases, i.e., nematic (N), smectic A (SmA), smectic B (SmB), and smectic G (SmG) phases. Both components of the thermal diffusivity show a dip at the second- or weakly first-order N-SmA phase transition due to the heat capacity anomaly. In contrast, at the first-order SmA-SmB phase transition, thermal diffusivity exhibits a stepwise increase. The x-ray and calorimetric measurements enable a calculation of the thermal conductivity and the study of the effect of the molecular length on the thermal conductivity and diffusivity in the SmA and SmB phases. For the homologues n = 4, 5, and 6, which exhibit the same phase sequence upon cooling, the parallel component of the thermal conductivity k(∥) in the SmA and SmB phases systematically increases with increasing length of the molecular tails, while no such increase is observed in the thermal diffusivity α(∥). We thus conclude that the molecular model [Urbach et al., J. Chem. Phys. 78, 5113 (1983)] is valid for the qualitative prediction of the effect of the molecular length on the magnitude of the thermal conductivity.

A Twist-Bend Nematic (NTB ) Phase of Chiral Materials.

New chiral dimers consisting of a rod-like and cholesterol mesogenic units are reported to form a chiral twist-bend nematic phase (NTB *) with heliconical structure. The compressibility of the NTB phase made of bent dimers was found to be as large as in smectic phases, which is consistent with the nanoperiodic structure of the NTB phase. The atomic force microscopy observations in chiral bent dimers revealed a periodicity of about 50 nm, which is significantly larger than the one reported previously for non-chiral compounds (ca. 10 nm).

Photonic Bandgap in Achiral Liquid Crystals-A Twist on a Twist.

Achiral mesogenic molecules are shown to be able to spontaneously assemble into liquid crystalline smectic phases having either simple or double-helical structures. At the transition between these phases, the double-helical structure unwinds. As a consequence, in some temperature range, the pitch of the helix becomes comparable to the wavelength of visible light and the selective reflection of light in the visible range is observed. The photonic bandgap phenomenon is reported for achiral liquid crystals.

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.

Multi-level chirality in liquid crystals formed by achiral molecules.

Complex materials often exhibit a hierarchical structure with an intriguing mechanism responsible for the 'propagation' of order from the molecular to the nano- or micro-scale level. In particular, the chirality of biological molecules such as nucleic acids and amino acids is responsible for the helical structure of DNA and proteins, which in turn leads to the lack of mirror symmetry of macro-bio-objects. To fully understand mechanisms of cross-level order transfer there is an intensive search for simpler artificial structures exhibiting hierarchical arrangement. Here we present complex systems built of achiral molecules that show four levels of structural chirality: layer chirality, helicity of a basic repeating unit, mesoscopic helix and helical filaments. The structures are identified by a combination of hard and soft x-ray diffraction measurements, optical studies and theoretical modelling. Similarly to many biological systems, the studied materials exhibit a coupling between chirality at different levels.

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.

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.

Polarization modulation instability in liquid crystals with spontaneous chiral symmetry breaking.

We present a theoretical model which describes the polarization-modulated and layer-undulated structure of the B7 phase and gives the phase transition from the synclinic ferroelectric smectic-C(S)P(F) phase to the B7 phase as observed experimentally. The system is driven into the modulated phase due to the coupling between the polarization splay and the tilt of the molecules with respect to the smectic layer normal. The modulation wavelength and the width of the wall between two domains of opposite chirality are estimated.

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.

Effect of spontaneous polarization and polar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells.

We use the Landau-de Gennes model to study theoretically the effect of the magnitude of the spontaneous polarization (P(S)), the ratio (r) between the equilibrium layer tilt and the smectic cone angle, the thickness of the insulating alignment layers and the strength of the polar and nonpolar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells with the chevron structure of smectic layers. The system shows a surprising number of stable structures, accompanied by one or two metastable ones. At P(S) greater than the critical value only quasimonostable structures, which can exhibit the thresholdless (V-shaped) switching, exist at all r and both at weak and strong polar surface anchoring. At lower P(S) bistable and monostable structures can coexist. Bistable structures can be expected at high r, low P(S) and if polar surface anchoring is weaker than the nonpolar one. Lowering the ratio r and/or increasing the strength of polar anchoring promotes the stability of monostable structures. Thicker insulating alignment layers also drive the system into the monostable state. Polar surface anchoring induces a large surface electroclinic effect. As a result the nematic deformations close to the surfaces are very strong and the stress is relieved by bending of the smectic layers. This leads to the formation of a double chevron structure which is stable at very large polar anchoring and due to the surface electroclinic effect it is metastable also at lower values of polar anchoring.