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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

Structure-sensitive bend elastic constants between piconewton and subnanonewton in diphenylacetylene-core-based liquid crystals.

Elastic constants in liquid crystals are known to be in the range of pico- and several-tens piconewton (pN). We report herein that a bend elastic constant, K33, remarkably varies depending on a slight modification of the chemical structure in an analogous series of calamitic liquid crystals. In contrast to the record-high bend elastic constants (hundreds pN or sub-nN) reported previously in a compound with an azo linkage, analogous compounds with tolan and ester linkages show several-tens pN and pN, respectively. X-ray diffraction studies of these compounds reveal that smectic-like layer structures (cybotacticclusters) are formed in the nematic phase of only the homologous compounds with an azo linkage, certifying the idea that the existence of cybotactic clusters strongly enhances K33. Two theoretical considerations were made: (1) Based on molecular conformation calculation, flat molecules that have high torsional potential energy, such as the one with an azo linkage, easily pack to form cybotactic clusters. (2) Theoretical estimation was made of how much cluster volume ratio is necessary to give about 100-times-larger K33s.

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)].

Effect of dimerization on the field-induced birefringence in ferrofluids.

The magnetic-field-induced birefringence in a ferrofluid composed of spherical cobalt nanoparticles has been studied both experimentally and theoretically. The considerable induced birefringence determined experimentally has been attributed to the formation of chains of nanoparticles. The birefringence has been measured as a function of the external magnetic field and the volume fraction (f) of nanoparticles. It is quadratic in f as opposed to the Faraday effect, which is linear in f. Experimental results agree well with the theoretical model based on a simple density functional approach. For dilute solutions the experimental results can be explained by assuming that only dimers of nanoparticles are formed while the concentration of longer chains is negligible.

Physical gels made of liquid crystalline B4 phase.

The achiral liquid crystalline materials showing two B4 (HN) phases have been found to exhibit strong gelation ability for various organic solvents with reversible sol-gel phase transition. The gel is formed by helical tubules, which build entangled 3D network, encapsulating the solvent. The equilibrium of left- and right-handed tubules is preserved in the gel, even if the chiral solvent is used.

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.