Spontaneous mirror symmetry breaking and chiral segregation in the achiral ferronematic compound DIO

An achiral compound, DIO, known to exhibit three nematic phases namely N, N_X and N_F, is studied by polarizing microscopy and electro-optics for different surface conditions in confinement. The high temperature N phase assigned initially as a conventional nematic phase, shows two additional unusual features: the optical activity and the linear electro-optic response related to the polar nature of this phase. An appearance of chiral domains is explained by the spontaneous symmetry breaking arising from the saddle-splay elasticity and followed by the formation of helical domains of the opposite chirality. This is the first example of helical segregation observed in calamitic non-chiral molecules in the nematic phase. As reported previously, the ferronematic N_F shows strong polar azimuthal surface interaction energy which stabilizes a homogeneous structure in planar aligned LC cells rubbed parallel and exhibits a twisted structure in cells with antiparallel buffing. The transmission spectra are simulated using Berreman's 4 × 4 matrix method. The observed agreement between the experimental and the simulated spectra quantitatively confirms the presence of twisted structures in antiparallel rubbed cells.

Structure and grating efficiency of thin cells filled by a twist-bend nematic liquid crystal

A twist-bend nematic (N_{TB}) liquid crystalline phase spontaneously forms modulated structures on a microscale level when confined in thin planar cells. Preliminary studies showed that these cells can be used as polarization gratings. Here we present a theoretical description of the formation of a two-dimensionally modulated structure. By considering the N_{TB} phase as a pseudolayer medium, a threshold condition for the onset of a modulated structure is calculated for weak and strong boundary conditions in the case of initially bookshelf or pretilt alignment of pseudolayers. Based on the modeled structure we determine spatial variation of the optic axis and calculate properties of the transmitted diffracted light. Results of the beam propagation method (BPM) and transfer matrix method are compared and it is shown that a more complex BPM gives better agreement with experimental results, meaning that even in thin cells the diffraction of light inside the grating should not be neglected.

Influence of tetrahedral order on ferromagnetic gel phases

We investigate the macroscopic dynamics of gels with tetrahedral/octupolar symmetry, which possess in addition a spontaneous permanent magnetization. We derive the corresponding static and dynamic macroscopic equations for a phase, where the magnetization is parallel to one of the improper fourfold tetrahedral symmetry axes. Apart from elastic strains, we take into account relative rotations between the magnetization and the elastic network. The influence of tetrahedral order on these degrees of freedom is investigated and some experiments are proposed that are specific for such a material and allow to indirectly detect tetrahedral order. We also consider the case of a transient network and predict that stationary elastic shear stresses arise when a temperature gradient is applied.

Ionic-surfactants-based thermotropic liquid crystals

Ionic surfactants can be combined with various functional groups through electrostatic interaction, resulting in a series of thermotropic liquid crystals (TLCs).

Formation and development of nanometer-sized cybotactic clusters in bent-core nematic liquid crystalline compounds

Two homologue achiral bent-core liquid crystals (LCs), BCN66 and BCN84, in their nematic phases are studied by dielectric spectroscopy in the frequency range 10 Hz-10 MHz. In each of these compounds, two relaxation processes are identified and assigned to (i) collective dynamics of molecules in nanometer-sized cybotactic clusters and (ii) individual molecular relaxations, in the ascending order of frequency of the probe field. The temperature and the bias electric field dependence of the dielectric strength and relaxation frequency for these processes are shown to give rise to sharpness in cluster boundaries, increased size and volume fraction in the LC nematic phase. The effect of the bias field on the LC cell is similar to reducing its temperature; both variables increase the cluster size and volume fraction and give rise to sharp cluster boundaries. The findings confirm that dielectric spectroscopy is a powerful and an extremely useful technique to provide a deeper understanding of the mechanism of cybotactic cluster formation in the isotropic liquid and the nematic phase of LCs as a function of temperature and the bias field.

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.

Chiral Structures from Achiral Micellar Lyotropic Liquid Crystals under Capillary Confinement

Recently, the emergence of spontaneous reflection-symmetry-broken configurations in achiral chromonic liquid crystals confined in cylindrical capillaries with homeotropic anchoring at the cylinder walls was reported, namely, the so-called twisted-escaped radial (TER) and twisted planar polar (TPP) configurations. This new example of spontaneous reflection symmetry breaking in liquid crystals was attributed to the twist elastic modulus, which is known to be unusually small in comparison to the splay and bend moduli in the case of chromonic liquid crystals. We now report the experimental observation of reflection symmetry breaking in cylindrical capillaries in the case of a classical, achiral, and nonchromonic lyotropic liquid crystal forming a nematic phase of disklike micelles orienting homeotropically at the capillary walls. We observed the same chiral TER configuration, as well as a nonplanar twisted polar (TP) configuration. The TP configuration is characterized by two half-unit so-called twist disclinations, where the director twist around the line defects drives the formation of a double helix of the disclinations along the axis of the capillary. Additionally, there is a transverse twist between the two disclination lines with the same handedness as the axial twist. Similarities with and differences from the case of chromonic liquid crystals are discussed; in particular, we examine the conditions under which spontaneous reflection symmetry breaking occurs in the nonchromonic system. It seems that the chiral TER configuration can be stabilized by the presence of point defects.

An Optically Isotropic Antiferroelectric Liquid Crystal (OI-AFLC) Display Mode Operating over a Wide Temperature Range using Ternary Bent-Core Liquid Crystal Mixtures

We report on the synthesis and characterization of bent-core liquid crystal (LC) compounds and the preparation of mixtures that provide an optically isotropic antiferroelectric (OI-AFLC) liquid crystal display mode over a very wide temperature interval and well below room temperature. From the collection of compounds synthesized during this study, we recognized that several ternary mixtures displayed a modulated SmCaPA phase down to below -40 °C and up to about 100 °C on both heating and cooling, as well as optical tilt angles in the transformed state of approximately 45° (optically isotropic state). The materials were fully characterized and their liquid crystal as well as electro-optical properties analyzed by polarized optical microscopy, differential scanning calorimetry, synchrotron X-ray diffraction, dielectric spectroscopy, and electro-optical tests.

On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order

We investigate the influence of transient or permanent elasticity on liquid phases with octupolar (tetrahedral) order, a question that has never been addressed before. The focus will be on optically isotropic liquid phases with tetrahedral order including the T _d phase and the chiral T phase introduced by Fel. It turns out that the presence of both, a network as well as tetrahedral order can lead to the formation of chiral domains of both hands in an optically isotropic fluid due to a completely novel mechanism, thus providing a possible macroscopic explanation for recent experimental observations. We study in detail how elasticity influences the macroscopic dynamics of both, the T _d and the T phase. The simultaneous presence of a transient network as well as of octupolar order is shown to lead to completely new cross-coupling phenomena for optically isotropic systems including transient dissipative elastic strains due to temperature gradients.

Orthogonal smectic and nematic ordering in three-ring polar bent-core molecules with anti-parallel arrangement

Three-ring based BLCs exhibiting orthogonal smectic and nematic phases with antiparallel arrangement as derived from SCXRD and X-ray scattering results.

Macroscopic behavior of polar nematic gels and elastomers

We present the derivation of the macroscopic equations for uniaxial polar nematic gels and elastomers. We include the strain field as well as relative rotations as independent dynamic macroscopic degrees of freedom. As a consequence, special emphasis is laid on possible static and dynamic cross-couplings between these macroscopic degrees of freedom associated with the network, and the other macroscopic degrees of freedom including reorientations of the macroscopic polarization. In particular, we find static and dissipative dynamic cross-couplings between strain fields and relative rotations on one hand and the macroscopic polarization on the other that allow for new possibilities to manipulate polar nematics. To give one example each for the effects of a static and a dissipative cross-coupling: we find that a static electric field applied perpendicularly to the polar preferred direction leads to relative rotations while dynamically relative rotations can lead to transverse electric currents. In addition to a permanent network, we also consider the effect of a transient network, which is particularly important for the case of gels, melts and concentrated polymer solutions. A section on the influence of macroscopic chirality is included as well.

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.

Local distortion energy and coarse-grained elasticity of the twist-bend nematic phase

The recently discovered twist-bend nematic phase of achiral bent-shaped molecules, NTB, has a doubly degenerate ground-state with a periodically modulated heliconical structure and unusual distortion elasticity, the theoretical description of which is still debated. We show that the NTB phase has the same macroscopic symmetry as another periodic mesophase, the chiral smectic-A, SmA*. Based on this NTB/SmA* analogy, we develop a coarse-grained elastic model for the NTB phase. Adopting one of the existing microscopic NTB elastic models, we calculate the coarse-grained elastic constants, coherence and penetration lengths in terms of a few Frank-like nematic elastic coefficients that can be measured in macroscopic experiments. The same coarse-grained approach, applied to different local elastic models, may provide an efficient experimental test of their validity. We show that the anisotropy of the NTB coarse-grained elasticity is opposite to that of the SmA*, leading probably to different configurations of some of the defects of the "layered" NTB structure. Moreover, we argue that the intrinsic chiral frustration of the NTB phase may be resolved by penetration of the twist field into the bulk through a network of screw dislocations of the NTB pseudo-layers, resulting in a twist-bend analogue of the twist grain boundary phase TGBA.

Spontaneous Mirror-Symmetry Breaking in Isotropic Liquid Phases of Photoisomerizable Achiral Molecules

Spontaneous mirror-symmetry breaking is of fundamental importance in science as it contributes to the development of chiral superstructures and new materials and has a major impact on the discussion around the emergence of uniform chirality in biological systems. Herein we report chirality synchronization, leading to spontaneous chiral conglomerate formation in isotropic liquids of achiral and photoisomerizable azobenzene-based rod-like molecules. The position of fluorine substituents at the aromatic core is found to have a significant effect on the stability and the temperature range of these chiral liquids. Moreover, these liquid conglomerates occur in a new phase sequence adjacent to a 3D tetragonal mesophase.

Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB–N phase transition

We have developed a Landau model that predicts a first order twist-bend nematic–nematic phase transition.

Chiral conglomerates observed for a binary mixture of a nematic liquid crystal trimer and 6OCB

Dark conglomerates of domains with opposite handedness, which are designated as dark conglomerate phases (DC phases), have attracted much attention. After designing an achiral liquid crystal trimer, 4,4′-bis{7-[4-(5-octyloxypyrimidin-2-yl)phenyloxy]heptyloxy}biphenyl (1), which exhibits only a nematic phase, we prepared binary mixtures with some typical rod-like nematic liquid crystals, i.e., 4′-hexyloxy-4-cyanobiphenyl (6OCB), 2-(4-hexyloxyphenyl)-5-pentyloxypyrimidine (PPY), or 4-methyloxyphenyl 4-hexyloxycyclohexanecarboxylate (PCA), and investigated their phase transition behaviour. The binary mixtures containing 55–90 mol% of 6OCB were found to exhibit a nematic phase and a DC phase of chiral domains with opposite handedness. However, neither PPY nor PCA induced such a chiral conglomerate phase in the mixture with trimer 1. We discuss how core–core interactions contribute to produce such a chiral conglomerate phase.

Spontaneous mirror symmetry breaking in a re-entrant isotropic liquid

An achiral double-swallow tailed tetracatenar compound forms a re-entrant isotropic liquid between a bicontinuous cubic phase and a nematic liquid crystalline phase. This isotropic liquid was found to represent a conglomerate of two immiscible chiral liquids. The chirality is retained and eventually becomes uniform at the transition to the cubic I432 phase.

Dark conglomerate phases of azobenzene derived bent-core mesogens - relationships between the molecular structure and mirror symmetry breaking in soft matter

New 4-bromoresorcinol based bent-core molecules with peripheral fluoro substituted azobenzene wings have been synthesized and the liquid crystalline self-assembly was investigated by differential scanning calorimetry (DSC), optical polarizing microscopy (POM), electro-optic studies and X-ray diffraction (XRD). A new type of optically isotropic mesophase composed of chiral domains with opposite handedness (dark conglomerate phases, DC phases) is observed, which for some homologues with medium alkyl chain length is stable down to ambient temperature. It is proposed that these DC phases are formed by helical twisted nano-domains of limited size and composed of the crystallized aromatic cores which are separated by the disordered alkyl chains. This structure is distinct from the previously known soft helical nano-filament phases (HNF phases, B4 phases) formed by extended crystalline nano-filaments and also distinct from the fluid sponge phases composed of deformed fluid layers. Comparison with related bent-core molecules having H, F, Cl, I, CH3 and CN groups in the 4-position at the resorcinol core, either with or without additional peripheral fluorines, provided information about the effects of these substituents on the tendency to form DC phases. Based on these relationships and by comparison with the minimum energy conformations obtained by DFT calculations a hypothesis is provided for the formation of DC phases depending on the molecular structure.

Flexoelectrically driven electroclinic effect in the twist-bend nematic phase of achiral molecules with bent shapes

We extend the twist-bend nematic (N(TB)) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field E applied perpendicular to the helix axis or wave vector q, with rotation of the N(TB) optic axis around E. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the N(TB) phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short (<10  nm) doubly degenerate pitch and ultrafast, submicrosecond response times.

Development of structural complexity by liquid-crystal self-assembly

Since the discovery of the liquid-crystalline state of matter 125 years ago, this field has developed into a scientific area with many facets. This Review presents recent developments in the molecular design and self-assembly of liquid crystals. The focus is on new exciting soft-matter structures distinct from the usually observed nematic, smectic, and columnar phases. These new structures have enhanced complexity, including multicompartment and cellular structures, periodic and quasiperiodic arrays of spheres, and new emergent properties, such as ferroelctricity and spontaneous achiral symmetry-breaking. Comparisons are made with developments in related fields, such as self-assembled monolayers, multiblock copolymers, and nanoparticle arrays. Measures of structural complexity used herein are the size of the lattice, the number of distinct compartments, the dimensionality, and the logic depth of the resulting supramolecular structures.

Chemically induced twist-bend nematic liquid crystals, liquid crystal dimers, and negative elastic constants

Here we report the chemical induction of the twist-bend nematic phase in a nematic mixture of ether-linked liquid crystal dimers by the addition of a dimer with methylene links; all dimers have an odd number of groups in the spacer connecting the two mesogenic groups. The twist-bend phase has been identified from its optical texture and x-ray scattering pattern as well as NMR spectroscopy, which demonstrates the phase chirality. Theory predicts that the key macroscopic property required for the stability of this chiral phase formed from achiral molecules is for the bend elastic constant to tend to be negative; in addition the twist elastic constant should be smaller than half the splay elastic constant. To test these important aspects of the prediction we have measured the bend and splay elastic constants in the nematic phase preceding the twist-bend nematic using the classic Frederiks methodology and all three elastic constants employing the dynamic light scattering approach. Our results show that, unlike the splay, the bend elastic constant is small and decreases significantly as the transition to the induced twist-bend nematic phase is approached, but then exhibits unexpected behavior prior to the phase transition.

A comparison of the conformational distributions of the achiral symmetric liquid crystal dimer CB7CB in the achiral nematic and chiral twist-bend nematic phases

The sets of residual dipolar couplings between carbon and hydrogen nuclei obtained from the proton-encoded (13)C 2D NMR experiment are used to investigate the conformational changes which occur when the achiral symmetric liquid crystal dimer CB7CB changes from the achiral nematic to the chiral twist-bend nematic phase. It is found that these changes are a consequence of the chirality of the twist-bend nematic phase, rather than being the driving force for the stability of this phase.

A liquid crystalline phase with uniform tilt, local polar order and capability of symmetry breaking

A new liquid crystalline (LC) phase with uniform tilt, local polar order and capability of symmetry breaking is found for a bent-core mesogen combining a 4-cyanoresorcinol unit with two azobenzene wings. The combination of local polar order and long range synclinic tilt in this SmC(s)P(R) phase leads, under special conditions, to macroscopic domains with opposite chirality, though the molecules themselves are achiral.

Chiral solutes can seed the formation of enantiomorphic domains in a twist-bend nematic liquid crystal

The twist-bend nematic, an enantiomorphic liquid-crystalline phase, exhibited by the structurally symmetric liquid-crystal dimer CB7CB is induced to form a single domain of uniform handedness, in the bulk, by the addition of the dopant chiral solute (S)-1-phenylethanol. Addition of a nonracemic (or scalemic) mixture of both R and S enantiomers of this solute produced equal volumes of P and M chiral domains for the twist-bend nematic phase. This seeding of the domains in an enantiomorphic nematic conglomerate is revealed using deuterium NMR spectroscopy.

A new family of four-ring bent-core nematic liquid crystals with highly polar transverse and end groups

Non-symmetrically substituted four-ring achiral bent-core compounds with polar substituents, i.e.., chloro in the bent or transverse direction in the central core and cyano in the lateral direction at one terminal end of the molecule, are designed and synthesized. These molecules possess an alkoxy chain attached at only one end of the bent-core molecule. The molecular structure characterization is consistent with data from elemental and spectroscopic analysis. The materials thermal behaviour and phase characterization have been investigated by differential scanning calorimetry and polarizing microscopy. All the compounds exhibit a wide-ranging monotropic nematic phase.

Molecular simulation of hierarchical structures in bent-core nematic liquid crystals

The structure of nematic liquid crystals formed by bent-core mesogens (BCMs) is studied in the context of Monte Carlo simulations of a simple molecular model that captures the symmetry, shape, and flexibility of achiral BCMs. The results indicate the formation of (i) clusters exhibiting local smectic order, orthogonal or tilted, with strong in-layer polar correlations and antiferroelectric juxtaposition of successive layers and (ii) large homochiral domains through the helical arrangement of the tilted smectic clusters, while the orthogonal clusters produce achiral (untwisted) nematic states.

Multiple electroconvection scenarios in a bent-core nematic liquid crystal

We report on the anisotropic electrohydrodynamic states formed over a wide temperature range (∼45 °C) in a planarly aligned bent-core nematic liquid crystal driven by fields of frequency in the range 0.1 Hz-1 MHz. Three different primary bifurcation scenarios are generated in the voltage-frequency (V-f) plane, depending on the temperature T. These, under increasing T, are characterized by the pattern sequences (i) in-plane longitudinal rolls (ILR)→in-plane normal rolls 1 (INR1), (ii) Williams rolls (WR)→ILR→INR1, and (iii) WR→INR2→INR1. Temperature-induced ILR→INR2 transition, the first example of its kind, points to elastic anisotropy as possibly the determining factor in wave vector selection. In the ILR and INR states, at threshold, the director modulations are predominantly azimuthal, and the streamlines, mainly normal to the wave vector, lie in the sample plane. Well above threshold, growing director deviations lead to narrow disclination loops that evolve in regular arrays, with their area density being exponential in voltage. The defects drift in a coordinated manner along the flow lines with a speed that scales nonlinearly with voltage; they mediate in the eventual occurrence of turbulence. The current theories of anisotropic convection based on static electrical parameters fail to account for the observed high-frequency instabilities. The study includes (i) a quantitative characterization of the critical parameter functions V(c)(f), V(c)(T), q(c)(f), and q(c)(T), with q(c) denoting the critical pattern wave number, and (ii) measurement of electrical and elastic parameters of relevance to electroconvection; the latter show anomalous features supporting the cluster hypothesis.

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D(2d) symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D (infinityh) nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D(2d) symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.