Spontaneous symmetry breaking in polar fluids.

Spontaneous symmetry breaking and emergent polar order are each of fundamental importance to a range of scientific disciplines, as well as generating rich phase behaviour in liquid crystals (LCs). Here, we show the union of these phenomena to lead to two previously undiscovered polar liquid states of matter. Both phases have a lamellar structure with an inherent polar ordering of their constituent molecules. The first of these phases is characterised by polar order and a local tilted structure; the tilt direction processes about a helix orthogonal to the layer normal, the period of which is such that we observe selective reflection of light. The second new phase type is anti-ferroelectric, with the constituent molecules aligning orthogonally to the layer normal. This has led us to term the phases the Sm C P H and SmAAF phases, respectively. Further to this, we obtain room temperature ferroelectric nematic (NF) and Sm C P H phases via binary mixture formulation of the novel materials described here with a standard NF compound (DIO), with the resultant materials having melting points (and/or glass transitions) which are significantly below ambient temperature. The new soft matter phase types discovered herein can be considered as electrical analogues of topological structures of magnetic spins in hard matter.

Structure-Property Relationships in Auxetic Liquid Crystal Elastomers-The Effect of Spacer Length.

Auxetics are materials displaying a negative Poisson's ratio, i.e., getting thicker in one or both transverse axes when subject to strain. In 2018, liquid crystal elastomers (LCEs) displaying auxetic behaviour, achieved via a biaxial reorientation, were first reported. Studies have since focused on determining the physics underpinning the auxetic response, with investigations into structure-property relationships within these systems so far overlooked. Herein, we report the first structure-property relationships in auxetic LCEs, examining the effect of changes to the length of the spacer chain. We demonstrate that for LCEs with between six and four carbons in the spacer, an auxetic response is observed, with the threshold strain required to achieve this response varying from 56% (six carbon spacers) to 81% (four carbon spacers). We also demonstrate that Poisson's ratios as low as -1.3 can be achieved. Further, we report that the LCEs display smectic phases with spacers of seven or more carbons; the resulting internal constraints cause low strains at failure, preventing an auxetic response. We also investigate the dependence of the auxetic threshold on the dynamics of the samples, finding that when accounting for the glass transition temperature of the LCEs, the auxetic thresholds converge around 56%, regardless of spacer length.

Toward Monodomain Nematic Liquid Crystal Elastomers of Arbitrary Thickness through PET-RAFT Polymerization.

Liquid crystal elastomers (LCEs) are polymeric materials that are proposed for a range of applications. However, to reach their full potential, it is desirable to have as much flexibility as possible in terms of the sample dimensions, while maintaining well-defined alignment. In this work, photoinduced electron/energy transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization is applied to the synthesis of LCEs for the first time. An initial LCE layer (∼100 µm thickness) is partially cured before a second layer of the precursor mixture is added. The curing reaction is then resumed and is observed by FTIR to complete within 15 min of irradiation, yielding samples of increased thickness. Monodomain samples that exhibit an auxetic response and are of thickness 250-300 µm are consistently achieved. All samples are characterized thermally, mechanically, and in terms of their order parameters. The LCEs have physical properties comparable to those of analogous LCEs produced via free-radical polymerization.

Room-temperature ferroelectric nematic liquid crystal showing a large and diverging density.

The ferroelectric nematic phase (NF) is a recently discovered phase of matter in which the orientational order of the conventional nematic liquid crystal state is augmented with polar order. Atomistic simulations suggest that the polar NF phase would be denser than conventional nematics owing to contributions from polar order. Using an oscillating U-tube densitometer, we obtain detailed temperature-dependent density values for a selection of conventional liquid crystals with excellent agreement with earlier reports. Having demonstrated the validity of our method, we then record density as a function of temperature for M5, a novel room-temperature ferroelectric nematic material. We present the first experimental density data for a NF material as well as density data for a nematic that has not previously been reported. We find that the room-temperature NF material shows a large (>1.3 g cm-3) density at all temperatures studied, notably including phases without polar order. An increase in density at phase transitions is observed. The magnitude of the increase for the intermediate-to-ferroelectric nematic (NX-NF) transition is an order of magnitude smaller than the isotropic-nematic (I-N) transition. We then probe potential consequences that may result from an elevated density through measurement of the refractive indices (no and ne). The navg of M5 is compared with 5CB and polar smectic liquid crystals. We observe how the highly polar nature of the system counteracts the effects of an increase in density. With knowledge of experimental density, we are able to derive an approximation that yields the polar order parameter, 〈P1〉, from polarisation measurements. Present results may be typical of ferroelectric nematic materials, potentially guiding material development, and is especially relevant for informing ongoing studies into this emerging class of materials.

Polarization patterning in ferroelectric nematic liquids via flexoelectric coupling.

The recently discovered ferroelectric nematic liquids incorporate to the functional combination of fluidity, processability and anisotropic optical properties of nematic liquids, an astonishing range of physical properties derived from the phase polarity. Among them, the remarkably large values of second order optical susceptibility encourage to exploit these new materials for non-linear photonic applications. Here we show that photopatterning of the alignment layer can be used to structure polarization patterns. To do so, we take advantage of the flexoelectric effect and design splay structures that geometrically define the polarization direction. We demonstrate the creation of periodic polarization structures and the possibility of guiding polarization by embedding splay structures in uniform backgrounds. The demonstrated capabilities of polarization patterning, open a promising new route for the design of ferroelectric nematic based photonic structures and their exploitation.

Dyes for guest-host liquid crystal applications: a general approach to the rapid computational assessment of useful molecular designs.

A set of experimental dichroic order parameters ranging from ca. +0.66 to -0.22 was obtained by recording polarized UV-visible absorption spectra from aligned samples of fifteen different guest anthraquinone and azo dyes in the nematic host 4-cyano-4'-pentylbiphenyl (5CB). DFT-optimised structures were calculated for between 1 and 16 conformers/tautomers of each dye, and their relative energies, UV-visible absorption wavelengths, oscillator strengths, transition dipole moments, molecular surface tensors and quadrupole tensors were obtained and used in subsequent calculations. A simple approach provided calculated UV-visible absorption spectra of the dyes that gave a qualitative match with the experimental spectra, and the calculated peak positions showed a linear correlation with the experimental values across the full visible range of ca. 350-700 nm. A short-range, shape-based, mean-field orienting potential based on the calculated surface tensors was combined with the calculated transition dipole moment vectors to give calculated dichroic ratios of the dyes that showed a linear correlation across the full range of experimental values. A modification of this mean-field orienting potential to include a long-range, electrostatic component based on the calculated quadrupole tensors gave a slightly improved linear correlation but a slightly worse overall match to the experimental values. The results show that short-range, shape-based interactions dominate the orienting potential for the systems studied here, with the inclusion of long-range quadrupole interactions providing a slightly better model for only some of the dyes. Overall, the use of a mean-field approach allied with molecular properties that can be calculated with relative ease and low computational expense has provided calculated peak positions and dichroic ratios that show good matches and correlations with experimental data from a variety of dye structures without the need to input any experimental data from the dyes. Hence, this method may provide a general and rapid approach to predicting the optical properties of dyes in liquid crystal hosts, enabling candidate dye structures to be screened prior to synthesis.

Implementation of a cylindrical distribution function for the analysis of anisotropic molecular dynamics simulations.

The cylindrical distribution function (CDF) is a convenient anisotropic analogue of the radial distribution function, the difference being the use of cylindrical shells for binning. As such, CDF analysis can be a powerful tool for the analysis of positional correlations within anisotropic systems, such as liquid crystals. Here we describe a lightweight Python tool, cylindr, for the calculation of cylindrical distribution function, which is compatible with the output of a number of popular MD engines. We demonstrate the use of cylindr in computing the CDF of a number of exemplar materials: classical and ferroelectric nematics; lamellar and columnar liquid crystals.

A new order of liquids: polar order in nematic liquid crystals.

Given the widespread adoption of display technology based on nematic liquid crystals, the discovery of new nematic phases at thermodynamic equilibrium, although extremely rare, generates much excitement. The remarkable discovery polar order and giant ferroelectric polarisation in a nematic fluid is a watershed moment in soft matter research, and is one of the most important discoveries in the 150 year history of liquid crystals. After a brief introduction to this emerging field, we present the current state-of-the art in terms of understanding the molecular origins of this phase, before exploring how molecular structure underpins the incidence of this phase, as well as exploring future directions.

A Ten-Year Perspective on Twist-Bend Nematic Materials.

The discovery of the twist-bend nematic phase (NTB) is a milestone within the field of liquid crystals. The NTB 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 NTB 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 NTB 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.

On the molecular origins of the ferroelectric splay nematic phase.

Nematic liquid crystals have been known for more than a century, but it was not until the 60s-70s that, with the development of room temperature nematics, they became widely used in applications. Polar nematic phases have been long-time predicted, but have only been experimentally realized recently. Synthesis of materials with nematic polar ordering at room temperature is certainly challenging and requires a deep understanding of its formation mechanisms, presently lacking. Here, we compare two materials of similar chemical structure and demonstrate that just a subtle change in the molecular structure enables denser packing of the molecules when they exhibit polar order, which shows that reduction of excluded volume is in the origin of the polar nematic phase. Additionally, we propose that molecular dynamics simulations are potent tools for molecular design in order to predict, identify and design materials showing the polar nematic phase and its precursor nematic phases.

Liquid Crystal Elastomers for Biological Applications.

The term liquid crystal elastomer (LCE) describes a class of materials that combine the elastic entropy behaviour associated with conventional elastomers with the stimuli responsive properties of anisotropic liquid crystals. LCEs consequently exhibit attributes of both elastomers and liquid crystals, but additionally have unique properties not found in either. Recent developments in LCE synthesis, as well as the understanding of the behaviour of liquid crystal elastomers-namely their mechanical, optical and responsive properties-is of significant relevance to biology and biomedicine. LCEs are abundant in nature, highlighting the potential use of LCEs in biomimetics. Their exceptional tensile properties and biocompatibility have led to research exploring their applications in artificial tissue, biological sensors and cell scaffolds by exploiting their actuation and shock absorption properties. There has also been significant recent interest in using LCEs as a model for morphogenesis. This review provides an overview of some aspects of LCEs which are of relevance in different branches of biology and biomedicine, as well as discussing how recent LCE advances could impact future applications.

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.

Insight into Out-of-Layer Fluctuations in the Smectic A Stability of 3,5-Diarylisoxazole Liquid Crystals.

Polar-terminated 3,5-diarylisoxazole liquid crystals (ILCs) were synthetized and characterized. ILCs are composed by rigid core 3,5-diarylisoxazol, alkyl chain and polar-terminated flexible spacer. Hydroxyl-, ketal- and 1,2-diol-terminated ILCs rendered smectic C and A mesophase, while bromine-terminated ILCs showed smectic A and B mesophase, for monosubstituted and linear ILCs. For branched alkyl chain monotropic SmA was detected and for disubstituted ILCs no mesophase was detected. Out-of-layer fluctuations (OLFs) are discussed based on X-ray diffraction date and textures. The OLFs are dependent on the bromine atom hardness, hydrogen bonding through collective actions and conformational effects at the interface between layers. Smectic translational order parameter (TOP) Σ was also obtained for orientated bromine- and hydroxyl-terminated ILCs and related it with OLFs. For 1,2-diol-terminated ILCs two SmC sublayers were founded, probably related to the intramolecular hydrogen bond favoring the 5-membered and 6-membered formation.

Ferroelectric-Ferroelastic Phase Transition in a Nematic Liquid Crystal.

Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes the formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5-10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory.

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

The nematic twist-bend (NTB ) 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 NTB 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.

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.

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.

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.

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 'NX ' 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 NX 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. The TB phase was first observed in low molecular weight dimers, and as such these have been the focus of efforts to understand the properties and structure of these new phases of matter. Recently several oligomeric and polymeric materials have been reported, but there is little information on the properties and structure of the TB phase in these materials. Herein we compare the order parameters, orientational distribution functions (ODF) and heliconical tilt angles of the TB phase exhibited by a liquid-crystalline dimer (CB7CB) to a tetramer (O47) and hexamer (O67) by SAXS/WAXS. Following the N-TB phase transition we find that all order parameters decrease, and while P2 remains positive P4 becomes negative. For all three materials the order parameter P6 is near zero in both phases. The ODF is sugarloaf-like in the nematic phase and volcano-like in the TB phase, allowing us to estimate the heliconical tilt angle of each material and its thermal evolution. Surprisingly, the heliconical tilt angle appears to be largely independent of the material studied despite the differing number of mesogenic units.