The dependency of twist-bend nematic liquid crystals on molecular structure: a progression from dimers to trimers, oligomers and polymers

13C CSA Tensors and Orientational Order of Model and Dimer Mesogens Comprising of Phenyl Benzoate

A Model mesogen and its symmetrical Dimer made up of phenyl benzoate core unit are investigated by 13C NMR spectroscopy. The existence of layer order in smectic A and smectic C phases of Dimer mesogen is established by powder X-ray diffraction. The chemical shift anisotropy (CSA) tensors of Model mesogen are determined by 2D separation of undistorted powder patterns by effortless recoupling (SUPER) experiment and are utilized for calculating the order parameters employing the alignment-induced chemical shifts (AIS). Additionally, 2D separated local field (SLF) NMR is availed for extracting 13C-1H dipolar couplings for both mesogens and used for computing the order parameters. A good agreement in the order parameters calculated from 13C-1H dipolar couplings and AIS is observed. Accordingly, the main order parameter (Szz) for the phenyl rings of the Model mesogen is found to be in the range 0.54-0.82, and for the Dimer mesogen, the values span 0.64-0.82 across mesophases. Since the phenyl benzoate core unit is frequently employed structural moiety for constructing the main chain as well as side chain liquid crystalline polymers and liquid crystalline elastomers, the CSA tensors reported here will be of immense utility for the structural characterization of these materials.

Useful synthetic artifacts? The impact of ubiquitous linker-adjacent groups on the self-assembly of discotic dimers

Although discotic dimers commonly feature bulky ether substituents adjacent to the linking group, the impact of these chains on self-assembly remains unclear. A series of dibenzo[a,c]phenazine dimers with alkoxy groups ortho to the linker were prepared and their solution conformational dynamics and liquid crystalline properties examined. The presence of a methoxy substitutent adjacent to the bridging group increased the phase stability, whereas longer chains dramatically decreased clearing temperatures. NMR solution studies indicated that adjacent groups increased the preference of dimers to adopt unfolded conformers. DFT models indicated that the unfolded structures were nonplanar and hence less compatible with columnar ordering, leading to a destabilization of the mesophases.

Liquid Crystal Dimers and the Twist-Bend Phases: Non-Symmetric Dimers Consisting of Mesogenic Units of Differing Lengths

The syntheses and characterisation of the 4-[{[4-({n-[4-(4-cyanophenyl)phenyl]-n-yl}oxy)phenyl]-methylidene}amino]phenyl-4-alkoxybenzoates (CBnOIBeOm) are reported with n=8 and 10 and m=1-10. The two series display fascinating liquid crystal polymorphism. All twenty reported homologues display an enantiotropic nematic (N) phase at high temperature. When the length of the spacer (n) is greater than that of the terminal chain (m), the twist-bend nematic (NTB) phase is observed at temperatures below the N phase. As the length of the terminal chain is increased and extends beyond the length of the spacer up to three smectic phases are observed on cooling the N phase. One of these smectic phases has been assigned as the rare twist-bend smectic C subphase, the SmCTB-α phase. In all the smectic phases, a monolayer packing arrangement is seen, and this is attributed to the anti-parallel associations of the like mesogenic units.

Comparative Study of the Optical and Dielectric Anisotropy of a Difluoroterphenyl Dimer and Trimer Forming Two Nematic Phases

We present a comparative study of the optical and dielectric anisotropy of a laterally fluorinated liquid crystal dimer and its homologous trimer, both exhibiting two nematic phases. In the high-temperature nematic phase, both oligomers exhibit positive optical anisotropy with similar magnitude, which, however, is lower in comparison with the optical anisotropy of the monomer. In the same temperature range, the dielectric permittivity along and perpendicular to the nematic director, measured on magnetically aligned samples, reveals negative dielectric anisotropy for both oligomers, which saturates as the temperature approaches the N-N phase transition temperature. Comparison of the dielectric anisotropies of the oligomers with the corresponding anisotropy of the monomer indicates a systematic variation of its magnitude with the number of the linked mesogenic units. Results are compared with the corresponding anisotropies of the cyanobiphenyl dimers, the archetypal compounds with two nematic phases, and are discussed in terms of the dipolar structure of the mesogens and the dipolar correlations in their nematic phases.

Effortless Extraction of Structural and Orientational Information from 13C-1H Dipolar Couplings for Thiophene Mesogens

Five molecular mesogens containing phenyl rings and thiophene are subjected to a detailed 13C NMR investigation. The first mesogen contains only phenyl rings, while the other four have thiophene with substitution at position 2 or 3. Two of these also have a spacer inserted between the thiophene and the rest of the core unit. The mesophase properties evaluated by complementary techniques reveal an enantiotropic nematic phase for all the cases and smectic C as well as Crystal J for a few mesogens. In addition to solution 13C NMR, the samples were studied using 1D and 2D solid-state 13C NMR experiments in the liquid crystalline phase. The chemical shifts and 13C-1H dipolar couplings obtained in the mesophase provided cutting-edge information about the molecular structure and orientation of the thiophene mesogens. Accordingly, dramatic differences in these parameters are noted for the mesogens, and consequently, the identification of 2- and 3-substituted thiophene mesogens is accomplished by a simple visual examination of the 2D spectra. Furthermore, for mesogens with a spacer between thiophene and the rest of the core, 13C chemical shifts and 13C-1H dipolar couplings showed remarkable variation, which was directly reflected in the order parameters. For instance, the order parameter (Szz) of thiophene in 2- and 3-substituted mesogens in which the spacer is absent is ∼0.63 whereas for those with spacer, it is reduced to ∼0.14-0.18. In comparison, the mesogen in which the core unit is made up of phenyl rings alone that is used to benchmark the characteristics of thiophene ordering showed an order parameter of ∼0.85. The study unambiguously demonstrates the supremacy of 13C NMR in extracting the structural and orientational information on mesogens in which thiophene is a constituent of the core unit.

Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies

The formation of the nematic to twist-bend nematic (NTB) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular interactions drive the complex twist-bend modulation observed in the NTB. The study employs broadband dielectric spectroscopy spanning frequencies from 10 to 2 × 109 Hz to investigate the molecular orientational dynamics within the glass-forming thioether-linked cyanobiphenyl liquid crystal dimers, namely, CBSC7SCB and CBSC7OCB. The experimental findings align with theoretical expectations, revealing the presence of two distinct relaxation processes contributing to the dielectric permittivity of these dimers. The low-frequency relaxation mode is attributed to an "end-over-end rotation" of the dipolar groups parallel to the director. The high-frequency relaxation mode is associated with precessional motions of the dipolar groups about the director. Various models are employed to describe the temperature-dependent behavior of the relaxation times for both modes. Particularly, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics in accordance with findings from infrared (IR) spectroscopy. Here, as the longitudinal correlations of dipoles intensify, the m1 mode experiences a sudden upsurge in enthalpy, while the m2 mode undergoes continuous changes, displaying critical mode coupling behavior. Interestingly, both types of molecular motion exhibit a strong cooperative interplay within the lower temperature range of the NTB phase, evolving in tandem as the material's temperature approaches the glass transition point. Consequently, both molecular motions converge to determine the glassy dynamics, characterized by a shared glass transition temperature, Tg.

Development of Donor-π-Acceptor-Type Fluorinated Tolanes as Compact Condensed Phase Luminophores and Applications in Photoluminescent Liquid-Crystalline Molecules

Fluorinated tolanes, produced by introducing fluorine atoms into one of the aromatic rings of tolane, emitted almost no fluorescence in a solution state, but the fluorescence intensity increased dramatically in the crystalline state because of intermolecular H⋅⋅⋅F hydrogen bonds. The photoluminescent (PL) colors depend on the molecular orbitals, dipole moments, and molecular aggregated structures can be varied by controlling terminal substituents along the major molecular axis. The introduction of a long alkoxy or semifluoroalkoxy unit as a flexible chain into the terminal positions along the major molecular axis induced the formation of a liquid-crystalline (LC) phase; fluorinated tolanes act both as luminophores and as mesogens, leading to the molecular design of new photoluminescent LC molecules (PLLCs). The results also indicated that a fluorinated tolane dimer, which consists of two fluorinated tolanes linked by a flexible alkylene spacer, also becomes a novel PLLC.

Conformational degrees of freedom and stability of splay-bend ordering in the limit of a very strong planar anchoring

We study the self-organization in a monolayer (a two-dimensional system) of flexible planar trimer particles. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend (S_{SB}) and chiral smectic-A (S_{A}^{*}) phases. The S_{SB} phase is also stable in the limit, where only cis- conformers are allowed. The second phase that occupies a considerable portion of the phase diagram is S_{A}^{*} with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis- conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the S_{A}^{*} phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay-bend (N_{SB}) phase for trimers, the free energy of the N_{SB} and S_{SB} phases is calculated within DFT for the cis- conformers, for densities where simulations show stable S_{SB}. It turns out that the N_{SB} phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of S_{SB}, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

How Do Intermolecular Interactions Evolve at the Nematic to Twist–Bent Phase Transition?

Polarized beam infrared (IR) spectroscopy provides valuable information on changes in the orientation of samples in nematic phases, especially on the role of intermolecular interactions in forming the periodically modulated twist–bent phase. Infrared absorbance measurements and quantum chemistry calculations based on the density functional theory (DFT) were performed to investigate the structure and how the molecules interact in the nematic (N) and twist–bend (N_TB) phases of thioether dimers. The nematic twist–bend phase observed significant changes in the mean IR absorbance. On cooling, the transition from the N phase to the N_TB phase was found to be accompanied by a marked decrease in absorbance for longitudinal dipoles. Then, with further cooling, the absorbance of the transverse dipoles increased, indicating that transverse dipoles became correlated in parallel. To investigate the influence of the closest neighbors, DFT calculations were performed. As a result of the optimization of the molecular cores system, we observed changes in the square of the transition dipoles, which well corresponds to absorbance changes observed in the IR spectra. Interactions of molecules dominated by pairing were observed, as well as the axial shift of the core to each other.

Study of the Experimental and Simulated Vibrational Spectra Together with Conformational Analysis of Thioether Cyanobiphenyl-Based Liquid Crystal Dimers

Infrared spectroscopy (IR) and quantum chemistry calculations that are based on the density functional theory (DFT) have been used to study the structure and molecular interactions of the nematic and twist-bend phases of thioether-linked dimers. Infrared absorbance measurements were conducted in a polarized beam for a homogeneously aligned sample in order to obtain more details about the orientation of the vibrational transition dipole moments. The distributions to investigate the structure and conformation of the molecule dihedral angle were calculated. The calculated spectrum was compared with the experimental infrared spectra and as a result, detailed vibrational assignments are reported.

Controlling spontaneous chirality in achiral materials: liquid crystal oligomers and the heliconical twist-bend nematic phase

Liquid crystal oligomers, namely dimers, trimers and tetramers, consisting of cyanobiphenyl and benzylideneaniline-based mesogenic units connected by either linear or bent alkoxy or alkyl spacers are reported. These materials, although built from achiral molecules, show the spontaneously chiral heliconical twist-bend nematic (N_TB) phase. We report the relationships between the shape of the oligomer, and the N_TB phase stability, the temperature dependence of the helical pitch length and tilt angle, birefringence, and elastic constants.

A Ten-Year Perspective on Twist-Bend Nematic Materials

The discovery of the twist-bend nematic phase (N_TB) is a milestone within the field of liquid crystals. The N_TB phase has a helical structure, with a repeat length of a few nanometres, and is therefore chiral, even when formed by achiral molecules. The discovery and rush to understand the rich physics of the N_TB phase has provided a fresh impetus to the design and characterisation of dimeric and oligomeric liquid crystalline materials. Now, ten years after the discovery of the N_TB phase, we review developments in this area, focusing on how molecular features relate to the incidence of this phase, noting the progression from simple symmetrical dimeric materials towards complex oligomers, non-covalently bonded supramolecular systems.

All-atom simulations of bent liquid crystal dimers: the twist-bend nematic phase and insights into conformational chirality

The liquid crystal dimer 1,7-bis-4-(4'-cyanobiphenyl)heptane (CB7CB) is known to exhibit a nematic-nematic phase transition, with the lower temperature phase identified as the twist-bend nematic (N_TB) phase. Despite the achiral nature of the mesogen, the N_TB phase demonstrates emergent chirality through the spontaneous formation of a helical structure. We present extensive molecular dynamics simulations of CB7CB using an all-atom force field. The N_TB phase is observed in this model and, upon heating, shows phase transitions into the nematic (N) and isotropic phases. The simulated N_TB phase returns a pitch of 8.35 nm and a conical tilt angle of 29°. Analysis of the bend angle between the mesogenic units reveals an average angle of 127°, which is invariant to the simulated phase. We have calculated distributions of the chirality order parameter, χ, for the ensemble of conformers in the N_TB and N phases. These distributions elucidate that CB7CB is statistically achiral but can adopt chiral conformers with no preference for a specific handedness. Furthermore, there is no change in the extent of conformational chirality between the N_TB and N phases. Using single-molecule stochastic dynamics simulations in the gas phase, we study the dimer series CBnCB (where n = 6, 7, 8 or 9) and CBX(CH₂)₅YCB (where X/Y = CH₂, O or S) in terms of the bend angle and conformational chirality. We confirm that the bent molecular shape determines the ability of a dimer to exhibit the N_TB phase rather than its potential to assume chiral conformers; as |χ|_max increases with the spacer length, but the even-membered dimers have a linear shape in contrast to the bent nature of dimers with spacers of odd parity. For CBX(CH₂)₅YCB, it is found that |χ|_max increases as the bend angle of the dimer decreases, while the flexibility of the dimers remains unchanged through the series.

All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals

The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely “shrinks down” established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (N_X), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist–bend nematic (N_TB). We show that the N_X is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the N_X phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the N_X and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank–Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist–bend, splay–bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the N_X phase. The latter modulation derives from packing constraints associated with nonlinear molecules—a chiral, locally-polar structural organization indicative of a new type of nematic phase.

Molecular biaxiality determines the helical structure - infrared measurements of the molecular order in the nematic twist-bend phase of difluoro terphenyl dimer

Fourier-transform infrared polarized spectroscopy was employed, to obtain the three components of the infrared absorbance for a series of bent-shaped dimers containing double fluorinated terphenyl core (DTC5Cn, n = 5, 7, 9, 11). The data were used to calculate both uniaxial and biaxial order parameters, for various molecular groups of dimers. The molecule bend was estimated based on the observed differences between the uniaxial order parameters for the terphenyl core and central hydrocarbon linker. The orientational order, distinctly reverses its monotonic trend of increase to decrease at the transition temperature, from the uniaxial nematic to the twist-bend nematic phase as result of the director tilt in latter/(twist-bend) phase. The molecular biaxiality, which is negligible in the nematic phase, starts increasing on entering the twist-bend nematic phase, following a sin-square relationships with the tilt angle. The local director curvature is found to be controlled by the molecular biaxiality parameter.

Twist-Bend Nematic Glasses: The Synthesis and Characterisation of Pyrene-based Nonsymmetric Dimers

A selection of pyrene-based liquid crystal dimers have been prepared, containing either methylene-ether or diether linked spacers of varying length and parity. All the diether linked materials, CBOnO.Py (n=5, 6, 11, 12), exhibit conventional nematic and smectic A phases, with the exception of CBO11O.Py which is exclusively nematic. The methylene-ether linked dimer, CBnO.Py, with an even-membered spacer (n=5) was solely nematogenic, but odd-members (n=6, 8, 10) exhibited both nematic and twist-bend nematic phases. Replacement of the cyanobiphenyl fragment by cyanoterphenyl giving CT6O.Py, gave elevated melting and nematic-isotropic transition temperatures, and SmA and SmC_A phases were observed on cooling the nematic phase. Intermolecular face-to-face associations of the pyrene moieties drive glass formation, and all these materials have a glass transition temperature at or above room temperature. The stability of the glassy twist-bend nematic phase allowed for its study using AFM, and the helical pitch length, P_TB , was measured as 6.3 and 6.7 nm for CB6O.Py and CB8O.Py, respectively. These values are comparable to the shortest pitch of a twist-bend nematic phase measured to date.

Experimental and Computational Study of a Liquid Crystalline Dimesogen Exhibiting Nematic, Twist-Bend Nematic, Intercalated Smectic, and Soft Crystalline Mesophases

Liquid crystalline dimers and dimesogens have attracted significant attention due to their tendency to exhibit twist-bend modulated nematic (NTB) phases. While the features that give rise to NTB phase formation are now somewhat understood, a comparable structure-property relationship governing the formation of layered (smectic) phases from the NTB phase is absent. In this present work, we find that by selecting mesogenic units with differing polarities and aspect ratios and selecting an appropriately bent central spacer we obtain a material that exhibits both NTB and intercalated smectic phases. The higher temperature smectic phase is assigned as SmCA based on its optical textures and X-ray scattering patterns. A detailed study of the lower temperature smectic ''X'' phase by optical microscopy and SAXS/WAXS demonstrates this phase to be smectic, with an in-plane orthorhombic or monoclinic packing and long (>100 nm) out of plane correlation lengths. This phase, which has been observed in a handful of materials to date, is a soft-crystal phase with an anticlinic layer organisation. We suggest that mismatching the polarities, conjugation and aspect ratios of mesogenic units is a useful method for generating smectic forming dimesogens.

Molecular Order of Topologically Variant Flexible Mesogens by 13C Nuclear Magnetic Resonance

¹³C nuclear magnetic resonance investigations in the nematic phase of mesogens comprising a rod-like core with three phenyl rings connected to a fourth phenyl ring via a flexible spacer are reported. The molecules are abbreviated as monomer, dimer, and trimer as they comprised one, two, and three pairs of core and spacer combinations linked to ring IV, respectively. Hot-stage optical polarizing microscopy and differential scanning calorimetry studies confirmed that all of them exhibit an enantiotropic nematic phase with additional monotropic or enantiotropic smectic mesophases. Large values of ¹³C-¹H dipolar couplings of the order of 11 kHz are observed for all the cases for the terminal carbon C1 of the core unit. These high values indicated that the corresponding CH vector is collinear with the long axis of the molecule, which itself is aligned parallel to the magnetic field. In contrast, the terminal carbon of the ring IV (C19/C17) exhibits a relatively smaller value in the range of 2.0-2.5 kHz, reflecting the divergent local dynamics at different sections of the mesogens. The orientational order parameters of the phenyl rings computed from the ¹³C-¹H dipolar couplings have been used to obtain the conformation of the mesogens in the nematic phase. It is concluded that the dimer and trimer exhibit C₂ and C₃ symmetry with the ring IV connected by spacers tilted away from the symmetry axis by 35.9 and 90^° for the two cases, respectively. This leads to the interesting tripod-like molecular shape for the trimer in the nematic phase rather than the planar representation of the λ shape.

Seeing the Unseen: The Role of Liquid Crystals in Gas-Sensing Technologies

Fast, real-time detection of gases and volatile organic compounds (VOCs) is an emerging research field relevant to most aspects of modern society, from households to health facilities, industrial units, and military environments. Sensor features such as high sensitivity, selectivity, fast response, and low energy consumption are essential. Liquid crystal (LC)-based sensors fulfill these requirements due to their chemical diversity, inherent self-assembly potential, and reversible molecular order, resulting in tunable stimuliresponsive soft materials. Sensing platforms utilizing thermotropic uniaxial systems-nematic and smectic-that exploit not only interfacial phenomena, but also changes in the LC bulk, are demonstrated. Special focus is given to the different interaction mechanisms and tuned selectivity toward gas and VOC analytes. Furthermore, the different experimental methods used to transduce the presence of chemical analytes into macroscopic signals are discussed and detailed examples are provided. Future perspectives and trends in the field, in particular the opportunities for LC-based advanced materials in artificial olfaction, are also discussed.

Role of molecular bend angle and biaxiality in the stabilization of the twist-bend nematic phase

What are the prerequisites for acquiring a stable twist-bend nematic phase (NTB)? Addressing this question has led to the synthesis of a vast number of new compounds, concluding each time that the molecule's shape is one of the predominant factors. Inspired by the expanding knowledge of different achiral bent-shaped molecules forming a twist-bend nematic phase, we reinvestigate the interplay between a molecule's bend angle and a molecule's arms molecular biaxiality. Employing our previously developed generalized mean-field model, we explore more obtuse bend angles. We observe direct phase transition sequences between locally biaxial and uniaxial variants of NTB, along with biaxial and uniaxial nematic phases. Additionally, we present a comprehensive overview of how phase diagrams evolve according to alterations in the value of the bend angle and the magnitude of biaxiality.

Stereochemical Rules Govern the Soft Self-Assembly of Achiral Compounds: Understanding the Heliconical Liquid-Crystalline Phases of Bent-Core Mesogens

A series of bent-shaped 4-cyanoresorcinol bisterephthalates is reported. Some of these achiral compounds spontaneously form a short-pitch heliconical lamellar liquid-crystalline phase with incommensurate 3-layer pitch and the helix axis parallel to the layer normal. It is observed at the paraelectric-(anti)ferroelectric transition, if it coincides with the transition from random to uniform tilt and with the transition from anticlinic to synclinic tilt correlation of the molecules in the layers of the developing tilted smectic phase. For compounds with long chains the heliconical phase is only field-induced, but once formed it is stable in a distinct temperature range, even after switching off the field. The presence of the helix changes the phase properties and the switching mechanism from the naturally preferred rotation around the molecular long axis, which reverses the chirality, to a precession on a cone, which retains the chirality. These observations are explained by diastereomeric relations between two coexisting modes of superstructural chirality. One is the layer chirality, resulting from the combination of tilt and polar order, and the other one is the helical twist evolving between the layers. At lower temperature the helical structure is replaced by a non-tilted and ferreoelectric switching lamellar phase, providing an alternative non-chiral way for the transition from anticlinic to synclinic tilt.

Utilising Saturated Hydrocarbon Isosteres of para Benzene in the Design of Twist-Bend Nematic Liquid Crystals

The nematic twist-bend (N_TB ) liquid crystal phase possesses a local helical structure with a pitch length of a few nanometres and is the first example of spontaneous symmetry breaking in a fluid system. All known examples of the N_TB phase occur in materials whose constituent mesogenic units are aromatic hydrocarbons. It is not clear if this is due to synthetic convenience or a bona fide structural requirement for a material to exhibit this phase of matter. In this work we demonstrate that materials consisting largely of saturated hydrocarbons can also give rise to this mesophase.

Coarse-grained model of the nematic twist-bend phase from a stable state elastic energy

The twist-bend nematic (N_{TB}) phase is a doubly degenerated heliconical structure with nanometric pitch and spontaneous bend and twist deformations. It is favored by symmetry-breaking molecular structures, such as bent dimers and bent-core molecules, and it is currently one of the burgeoning fields of liquid-crystal research. Although tremendous advances have been reported in the past five years, especially in molecular synthesis, most of its potential applications are held back by the lack of a proper and definitive elastic model to describe its behavior under various situations such as confinement and applied field. In this work we use a recently proposed stable state elastic model and the fact that the mesophase behaves as a lamellar structure to propose a mesoscopic or coarse-grained model for the N_{TB} phase. By means of standard procedures used for smectic and cholesteric liquid crystals, we arrive at a closed-form energy for the phase and apply it to a few situations of interest. The predicted compressibility for several values of the cone angle and the critical field for field-induced deformation agree well with recent experimental data.

Chemically induced splay nematic phase with micron scale periodicity

Nematic liquid crystals lack positional order of their constituent molecules, which share an average orientational order only. Modulated nematic liquid crystal phases also lack positional order, but possess a periodic variation in this direction of average orientation. In the recently discovered splay nematic (NS) phase the average orientational order is augmented with a periodic splay deformation of orientation perpendicular to the director. In this communication we report the first example of a splay nematic phase which is chemically induced by mixing two materials, neither of which exhibit the NS phase. The splay-nematic phase is identified based on its optical textures, X-ray scattering patterns, and small enthalpy of the associated phase transition. We measure the splay periodicity optically, finding it to be ∼9 μm. This unexpected generation of the splay-nematic phase through binary mixtures offers a new route to materials which exhibit this phase which complements ongoing studies into structure-property relationships and could accelerate the development of technologies utilising this remarkable polar nematic variant.

Uniform distortions and generalized elasticity of liquid crystals

Ordinary nematic liquid crystals are characterized by having a uniform director field as ground state. In such a state, the director is the same everywhere and no distortion is to be seen at all. We give a definition of uniform distortion which makes precise the intuitive notion of seeing everywhere the same director landscape. We characterize all such distortions and prove that they fall into two families, each described by two scalar parameters. Uniform distortions exhaust R. Meyer's heliconical structures, which, as it has recently been recognized, include the ground state of twist-bend nematics. The generalized elasticity of these new phases is treated with a simple free-energy density, which can be minimized by both uniform and nonuniform distortions, the latter injecting a germ of elastic frustration.

Molecular Flexibility and Bend in Semi-Rigid Liquid Crystals: Implications for the Heliconical Nematic Ground State

The NTB phase phases possess a local helical structure with a pitch length of a few nanometers and is typically exhibited by materials consisting of two rigid mesogenic units linked by a flexible oligomethylene spacer of odd parity, giving a bent shape. We report the synthesis and characterisation of two novel dimeric liquid crystals, and perform a computational study on 10 cyanobiphenyl dimers with varying linking groups, generating a large library of conformers for each compound; this allows us to present molecular bend angles as probability weighted averages of many conformers, rather than use a single conformer. We validate conformer libraries by comparison of interproton distances with those obtained from solution-based 1D 1 H NOESY NMR, finding good agreement between experiment and computational work. Conversely, we find that using any single conformer fails to reproduce experimental interproton distances. We find the use of a single conformer significantly overestimates the molecular bend angle while also ignoring flexibility; in addition, we show that the average bend angle and flexibility are both linked to the relative stability of the NTB phase.

Dielectric response of electric-field distortions of the twist-bend nematic phase for LC dimers

Wide band dielectric spectroscopy of bent-shaped achiral liquid-crystal dimers 1″-n″-bis(4-cyanobiphenyl-4'-yl) n-alkanes (CBnCB n = 7, 9, 11) has been investigated in a frequency range 0.1 Hz-100 MHz using planar-aligned cells of sample thicknesses ranging from 2 to 10 (μm) over a temperature range that covers both nematic and twist bend nematic phases. Two peaks in the dielectric spectrum in the higher frequency range are assigned to the molecular relaxation processes. The peak at the highest frequency, ∼40 to 80 MHz, is assigned to an internal precessional rotation of a single unit of the dimer around the director. The mode in the next lower frequency range of 2-10 MHz is assigned to the spinning rotation of the dimer around its long axis. This involves fluctuations of the dipole moment of the bent-shaped conformation that is directed along its arrow direction of the bow shape formed by the dimer. The peak in the frequency range 100 kHz-1 MHz can be assigned to the collective fluctuations of the local director with reference to the helical axis of the N_TB structure. The dependence of its frequency on temperature is reminiscent of the soft mode observed at the SmA^* to SmC^* phase transition. This result clearly corresponds to the electro-clinic effect-the response of the director to the applied electric field in an electro-optic experiment. The lowest frequency mode, observed in the frequency range of 0.1 Hz-100 Hz, is identified with the Goldstone mode. This mode is concerned with the long range azimuthal angle fluctuations of the local director. This leads to an alternating compression and expansion of the periodic structure of the N_TB phase.

Pentaerythritol Derived Tetrapode Exhibiting a Nematic-Like Mesophase at Ambient Temperatures

The nematic liquid-crystalline phase exhibits average orientational order, with no positional organisation. So-called modulated nematic phases exhibit this same orientational order with an additional spatially periodic modulation of the nematic director, the most common of which is the twist-bend nematic phase. We report a pentaerythritol derived tetrapode which exhibits a nematic-like mesophase at ambient temperature, and we denote this new mesophase 'N_X ' to indicate a nematic phase of unknown structure. X-ray scattering experiments refute the possibility of positional order, yet optical textures are consistent with a periodic structure. We suggest that the mesophase exhibited by this material is a new type of nematic-like mesophase with some form of modulated structure. We find the N_X phase to exhibit an electrooptic response consistent with a nematic-like phase.

Order parameters, orientational distribution functions and heliconical tilt angles of oligomeric liquid crystals

Twist-bend (TB) phases possess a local helical structure with a pitch length of a few nanometers. X-ray scattering experiments on aligned samples of dimeric and oligomeric materials allows the orientational order parameters, orientational distribution functions and heliconical tilt angles to be calculated.

Pretransitional behavior of viscoelastic parameters at the nematic to twist-bend nematic phase transition in flexible n-mers

We report dynamic light scattering measurements of the orientational (Frank) elastic constants and associated viscosities among a homologous series of a liquid crystalline dimer, trimer, and tetramer exhibiting a uniaxial nematic (N) to twist-bend nematic (N_TB) phase transition.

Orientational order in the splay nematic ground state

Modulated nematic liquid crystal phases, which lack positional order but have some periodic variation in the direction of average orientation present in a classical nematic, have attracted significant interest. In the recently discovered splay nematic (NS) phase the average orientational order is augmented with a periodic splay deformation of orientation perpendicular to the director. We use X-ray scattering experiments to measure the orientational order parameters in the nematic (N) and splay nematic (NS) phases of the liquid crystalline material RM734. The degree of orientational order is somewhat larger in the NS phase than in the preceding nematic and temperature dependent. We reconstruct the orientational distribution function and find it to be nematic-like in the NS phase, indicating the change in orientation between neighbouring molecules due to the splay modulation is very small. A small splay angle implies that the splay modulation period is larger than the few tens of nanometers originally envisaged. The method described herein can be used to assist in unambiguous identification of the splay-nematic phase.

Highly frustrated liquid crystal phases in optically active dimers: synthesis and rich phase transitional behavior

New cholesterol-based Schiff base dimers exhibit a rich mesomorphism.

A novel nematic-like mesophase induced in dimers, trimers and tetramers doped with a high helical twisting power additive

From the observation of a previously undiscovered nematic-like mesophase (NX) by Archbold et al., we report on several new binary liquid-crystalline mixtures between the high helical twisting power dopant RM1041 and a selection of dimers with varying average bend angles and conformational landscapes. We also report on mixtures between RM1041 and oligomeric LC materials. We find that dimers and oligomers exhibit not only chiral nematic and twist-bend modulated phases, but also the same NX phase reported by Archbold, indicating that this state of matter (the structure of which is yet to be definitively characterised) is exhibited by a wide range of materials. Mixtures of the dimer CB9CB with a selection of different chiral dopants suggest that it is the helical twisting power of the chiral additive that is responsible incidence of the NX phase.

Fine-tuning the effect of π-π interactions on the stability of the NTB phase

The synthesis and liquid-crystalline properties are reported for novel bent-shaped dimers in which a naphthyl group has been incorporated into the mesogenic cores. In addition to the nematic and twist-bend nematic phase, a new liquid-crystalline phase was observed. The combined experimental and computational study demonstrated how the interplay between the molecular geometry and π-π interactions affects the thermal stability of the twist-bend nematic and nematic phases. Correlation between mesomorphic properties and molecular geometry revealed that a greater conformational diversity leads to a broader distribution of bend-angles and destabilization of the NTB phase. Qualitative correlation between the thermal behaviour and electronic structure of the molecules of a similar geometry suggested that the transition temperatures of both nematic phases depend on the relative contribution of dispersion and electrostatic energies which determines the strength of the π-π interactions. These results provide an insight into how subtle changes in chemical structure can be exploited to tune the intermolecular interactions and influence the thermal stability of the liquid crystalline phase.

Supramolecular organization of liquid-crystal dimers - bis-cyanobiphenyl alkanes on HOPG by scanning tunneling microscopy

2D supramolecular organization of a series of six cyanobiphenyls bimesogens deposited on highly oriented pyrolytic graphite (HOPG) is studied by scanning tunneling microscopy (STM). The adsorbates are 1,ω-bis(4-cyanobiphenyl-4'-yl)alkanes (CBnCB) with different lengths of their flexible alkyl spacer (containing from 7 to 12 methylene groups). Microscopic investigations at the molecular resolution allow for detailed analysis of the effect of the alkyl spacer length on the type and the extent of the resulting 2D organization. It was demonstrated that bimesogens with shorter spacers (7 and 8 methylene units) organize in a similar manner characterized by the formation of two types of differently ordered monolayers: dense packed, wherein the molecules are oriented in one direction and ordered into parallel rows (layer structure), or less densely packed where they are organized into a chiral windmill-like structure. For derivatives with longer spacers (ranging from 9 to 12 methylene units) the additional effect of parity of carbon atoms in the spacer (even versus odd) is observed. In this range of the spacer lengths even membered bimesogens are also organized in a typical layer structure. However, odd-membered dimers exhibit a much more complex 2D supramolecular organization with a larger unit cell and a helical arrangement of the molecules. Careful comparison of this structure with the 3D structural data derived from the X-ray diffraction investigations of single crystals indicates that for these bimesogens a clear correlation exists between the observed complex 2D supramolecular organization in the monolayer and the organization in one of the crystallographic planes of the 3D nematic twist-bent phase.

A Nanohelicoidal Nematic Liquid Crystal Formed by a Non-Linear Duplexed Hexamer

The twist-bend modulated nematic liquid-crystal phase exhibits formation of a nanometre-scale helical pitch in a fluid and spontaneous breaking of mirror symmetry, leading to a quasi-fluid state composed of chiral domains despite being composed of achiral materials. This phase was only observed for materials with two or more mesogenic units, the manner of attachment between which is always linear. Non-linear oligomers with a H-shaped hexamesogen are now found to exhibit both nematic and twist-bend modulated nematic phases. This shatters the assumption that a linear sequence of mesogenic units is a prerequisite for this phase, and points to this state of matter being exhibited by a wider range of self-assembling structures than was previously envisaged. These results support the double helix model of the TB phase as opposed to the simple heliconical model. This new class of materials could act as low-molecular-weight surrogates for cross-linked liquid-crystalline elastomers.

Optically active bimesogens incorporating branched central spacers

In the current fascination with liquid crystalline dimers, bimesogens and oligomers the role of the central spacer in these systems has perhaps been somewhat neglected. In compound 1, a phenyl 4-cyanobenzoate bimesogen, the central spacer incorporates a methyl group at the 2-position and is therefore chiral. The helical twisting power of 1, measured in both 5CB and E7, was found to be 0.36 and 0.35 μm-1 wt%-1 respectively. Compound 1 exhibited a monotropic chiral nematic phase, however no twist-bend modulated phase was observed. We prepared a number of analogues of 1 incorporating different mesogenic units and observe that those with a small aspect ratio are non mesogenic, whereas those with larger aspect ratios variously exhibit chiral nematic, TB, SmC and SmB phases.

Induced smectic phase in binary mixtures of twist-bend nematogens

The investigation of liquid crystal (LC) mixtures is of great interest in tailoring material properties for specific applications. The recent discovery of the twist-bend nematic phase (N_TB) has sparked great interest in the scientific community, not only from a fundamental viewpoint, but also due to its potential for innovative applications. Here we report on the unexpected phase behaviour of a binary mixture of twist-bend nematogens. A binary phase diagram for mixtures of imino-linked cyanobiphenyl (CBI) dimer and imino-linked benzoyloxy-benzylidene (BB) dimer shows two distinct domains. While mixtures containing less than 35 mol % of BB possess a wide temperature range twist-bend nematic phase, the mixtures containing 55-80 mol % of BB exhibit a smectic phase despite that both pure compounds display a Iso-N-N_TB-Cr phase sequence. The phase diagram shows that the addition of BB of up to 30 mol % significantly extends the temperature range of the N_TB phase, maintaining the temperature range of the nematic phase. The periodicity, obtained by atomic force microscopy (AFM) imaging, is in the range of 6-7 nm. The induction of the smectic phase in the mixtures containing 55-80 mol % of BB was confirmed using polarising optical microscopy (POM), differential scanning calorimetry (DSC) and X-ray diffraction. The origin of the intercalated smectic phase was unravelled by combined spectroscopic and computational methods and can be traced to conformational disorder of the terminal chains. These results show the importance of understanding the phase behaviour of binary mixtures, not only in targeting a wide temperature range but also in controlling the self-organizing processes.

Twist-bend nematic phase in biphenylethane-based copolyethers

The main-chain liquid crystal (LC) copolyethers in which the nematic-nematic phase transition was first experimentally observed were revisited and re-characterised. Grazing incidence X-ray scattering revealed that the low-T nematic (Ntb) phase could be highly aligned by shearing, more so than in previously studied bent LC dimers. This was evidenced by a four-point wide-angle X-ray scattering pattern, which originates from convolution of two tilt distributions. Through intensity simulation the orientational order parameter associated with each of the distributions, as well as the conical angle of the Ntb phase, was calculated. Information regarding the polymer chain conformation was obtained using polarised infrared spectroscopy. The findings suggest the average conformation of the chains is a helix, and that the bend angle between mesogenic units is inversely related to temperature. All experimental evidence, including a jump in birefringence at the Ntb-nematic (N) phase transition, shows that copolyether samples mirror the behaviour of bent LC dimers over the transition. This confirms that the low-T nematic phase in copolyethers is indeed the same as that in LC dimers, now known to be the Ntb. The unusual broadening of transition peaks in complex heat capacity, obtained by modulated DSC experiments, is discussed.

Spontaneous chirality through mixing achiral components: a twist-bend nematic phase driven by hydrogen-bonding between unlike components

The spontaneous formation of a chiral phase via molecular recognition in a system consisting of achiral components is reported. Specifically, the liquid crystalline behaviour of two molecular complexes assembled by hydrogen bonding between a stilbazole-based template and alkoxybenzoic acids has been characterised. The complexes exhibit the heliconical twist-bend nematic phase (NTB) over a broad temperature range despite the hydrogen-bond acceptor not being liquid crystalline and the donor exhibiting the conventional achiral nematic phase.