Landau theory for uniaxial nematic,biaxial nematic,uniaxial smectic-A,and biaxial smectic-A phases

We use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes continuous. The four phases meet at a tetracritical point.     

X-ray diffraction from the uniaxial and biaxial nematic phases of bent-core mesogens

X-ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent-core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X-ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X-ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial-biaxial phase transition, and estimate the order parameters of the nematic phase.     

X‐ray diffraction from the uniaxial and biaxial nematic phases of bent‐core mesogens

X‐ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent‐core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X‐ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X‐ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial–biaxial phase transition, and estimate the order parameters of the nematic phase.     

Helical twisting power and compatibility in twisted nematic phase of new chiral liquid crystalline dopants with various liquid crystalline matrices

ABSTRACT

Four chiral dopants exhibiting smectic LC phases themselves were prepared and their helical twisting power (HTP) and thermal phase behaviour in mixtures with four various LC hosts were studied. The influence of host liquid crystal on HTP was evaluated and generally higher values were found for hosts with high birefringence. Unexpectedly, high enhancement was found for an LC-chiral dopant pair, both having a similar aromatic core – biphenyl ring substituted with polar group. All studied chiral dopants exhibited limited compatibility with the LC hosts in twisted nematic phase at room temperature. For one of the studied mixtures, it was able to obtain single twisted nematic phase with selective light reflection band with maximum at wavelength about 1.0 µm. Carboxylic acid-type dopants exhibited total compatibility with the studied host in single twisted nematic phase at elevated temperatures, allowing preparation of mixtures with reflection band in the visible range. In case of the carboxylic acid dopants, blue phases for optimised compositions were observed. Intermolecular hydrogen bonding between carboxylic acid proton and pyridine nitrogen of chiral dopants was found. Doping the LC host with these dopants led to slight enhancement of HTP value and higher solubility in the LC host.     

Thermotropic biaxial nematic liquid crystals: spontaneous or field stabilized?

An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematic liquid crystals. The phase is macroscopically uniaxial but has microscopic biaxial, and possibly polar, domains. Under the action of an electric field, the phase acquires macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.     

The twist-bend nematic phase: translational self-diffusion and biaxiality studied by 1H nuclear magnetic resonance diffusometry

ABSTRACT

Recently, there has been a surge of interest in mesogens exhibiting the twist-bend nematic (N_TB) phase that is shown to be chiral even though formed by effectively achiral molecules. Although it now seems to be clear that the N_TB phase in the bulk is formed by degenerate domains having opposite handedness, the presence of a supramolecular heliconical structure proposed in the Dozov model has been contradicted by the Hoffmann et al. model in which the heliconical arrangement is replaced by a polar nematic phase. The evidence in support of this is that the quadrupolar splitting tensor measured in various experiments is uniaxial and not biaxial as expected for the twist-bend nematic structure. In this debate, among other evidence, the molecular translational diffusion, and its magnitude with respect to that in the nematic phase above the N_TB phase, has also been invoked to eliminate or to confirm one model or the other. We attempt to resolve this issue by reporting the first measurements of the translational self-diffusion coefficients in the nematic and twist-bend nematic phases formed 1″,7″-bis-4-(4′-cyanobiphenyl-4′-yl) heptane (CB7CB). Such measurements certainly appear to resolve the differences between the two models in favour of that for the classic twist-bend nematic phase.     

Landau theory-based estimates for viscosity coefficients of uniaxial and biaxial nematic liquid crystals

Using Landau theory, it is shown that eight phenomenological parameters are needed to describe and distinguish the twelve viscosity coefficients of a biaxial nematic phase, or the five viscosity coefficients of a uniaxial nematic phase. The dependence of the coefficients on the macroscopic uniaxial and biaxial order parameters is established. Since these order parameters are determined by the anisotropies of the dielectric constant, we show that it should be possible to determine values for all eight of the phenomenological parameters of the theory from measurements of the temperature dependence of the five viscosities of a uniaxial phase.     

Enantiotropic Nematics From Cross‐Like 1,2,4,5‐Tetrakis(4′‐alkyl‐4‐ethynylbiphenyl)benzenes and Their Biaxiality Studies

The theoretically predicted optimum length/breadth/width ratio for maximizing shape biaxiality was investigated experimentally by the facile and successful synthesis of cross‐shaped compound 3 , which showed enantiomeric nematic phase behavior. This cross‐like core structure could alternatively be viewed as two fused V‐shaped mesogens, which have recently immerged as a new direction in biaxial nematic research, at the bending tips that can act as a new structure for biaxial investigations. Whilst the thermal analysis data of compound 3 did not meet the expected theoretical values for biaxial nematics, surface‐induced biaxiality was evidenced by optical studies. Cluster‐size analysis within the nematic phase of compound 3 revealed the formation of meta‐cybotactic nematics, which approached the cluster sizes of cybotactic nematics. The split small‐angle 2D X‐ray diffraction patterns of magnetic‐field‐aligned samples indicated that the nematic phase was composed of small smectic C‐like clusters with the tilting of molecules within the clusters. The wide‐temperature‐range enantiomeric nematic phase of cross‐like compound 3 enabled the molecular skeleton to serve as an alternative skeleton to bent‐rod mesogens, which exhibited nematic phases with the potential competition of transitions to higher‐order liquid‐crystalline phases and crystallization, for future biaxial investigations.     

To be or not to be – nematic liquid crystals from shape-persistent V-shaped nematogens with the ‘magic angle’

The tetrahedral bending angle in V-shaped nematogens was claimed to be the optimum for finding a biaxial nematic liquid crystal phase. The benzo[1,2-b:4,3-b’]dithiophene core, recently successfully applied as a tetrahedral bending unit in mesogens with lateral flexible chains, is here embedded in a scaffold with only terminal chains, which conventionally promotes the formation of nematic phases at low temperature. A series of new mesogens has been successfully prepared, realising hockey-stick, hockey-stick dimer and V-shaped molecular topologies. Only the hockey-stick mesogens assemble in uniaxial nematic phases over a broad temperature range. Single crystal structure analysis of a hockey-stick and V-shaped compound reveal remarkable similarities with the benzodithiophene core wrapped by aliphatic chains. A model explaining the absence of nematic mesophases in the family of V-shaped, shape-persistent mesogens with terminal aliphatic chains is presented and results in the proposal of a new design for biaxial nematogens.     

On the Uniaxial–Biaxial Nematic Phase Transition in Liquid‐Crystalline Polymers and Elastomers

We study how the uniaxial–biaxial nematic phase transition changes its nature when going from a low‐molecular‐weight liquid crystal to a liquid‐crystalline elastomer or polymer (the latter above the Maxwell frequency) and find a qualitative change due to the presence of a coupling to the strain field in these materials. While this phase transition can be of second‐order in low‐molecular‐weight materials, as is also experimentally observed, we show here that the order of this phase transition is changed generically to no phase transition at all or to a first‐order phase transition in mean‐field approximation. We analyze the influence of an external mechanical stress field above the uniaxial–biaxial nematic phase transition and find that either biaxial nematic order is induced, which is linear or quadratic in the stress intensity, or no response to an external stress results at all, depending on the relative orientation of the applied shear with respect to the director of the uniaxial nematic phase.     

Preorganised effects of a tetramesogenic supermolecule on supramolecular assembly in the liquid crystalline phases

After preparing a homologous series of tetrameric mesogenic compounds in which two U-shaped molecules were connected via a rigid benzene derivative or a flexible alkyl chain, we investigated their phase transition behaviour using optical microscopy, differential scanning calorimetry and X-ray diffraction analysis. The compounds possessing an alkyl spacer as the central group exhibited nematic and smectic A phases just as the corresponding U-shaped molecule did. The compound possessing a 1,2-benzene unit as the connecting group showed nematic and smectic A phases, although the compound possessing a 1,3-benzene unit exhibited only an anticlinic smectic C phase. Structure–property relations of the liquid crystalline tetramers are interpreted in terms of preorganised effects of the four mesogenic units.     

Bifurcational analysis of the isotropic-discotic nematic phase transition in the presence of extensional flow

A bifurcational analysis is performed on a version of Doi's equation of nematodynamics that describes the non-equilibrium isotropic-discotic nematic phase transition in the presence of steady uniaxial extensional flow. The disc-like molecular geometry and the degenerate extensional flow-induced orientation are shown to be the source of a complex bifurcation and multistability behaviour involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. Depending on the temperature and the extension rate, the isotropic-discotic nematic transition, involving the two biaxial nematic phases and the uniaxial paranematic phase, may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. A validation procedure on the validity of the predictions is implemented. The predictions presented here find practical applications in the industrial spinning of mesophase carbon fibres, and also provide new results that increase the present fundamental understanding of the rheology of discotic nematic liquid crystals.     

Thermotropic uniaxial and biaxial nematic and smectic phases in bent-core mesogens

Two azo substituted achiral bent-core mesogens have been synthesized. Optical polarizing microscopy and synchrotron X-ray scattering studies of both compounds reveal the existence of the thermotropic uniaxial and biaxial nematic and three smectic phases at different temperatures in these single component small molecule systems. The transition from the uniaxial to biaxial nematic phase is confirmed to be second order. The transitions from the biaxial nematic to the underlying smectic phase and between the smectic phases have barely discernible heat capacity signatures and thus are also second order.     

Phase diagrams of binary mixtures of biaxial nematogens

A mean field theory is used to describe nematic phases of binary mixtures of biaxial molecules. Using a general pseudopotential consistent with the D_2h symmetry of the constituent particles, the theory is used to calculate the elements of the order tensors necessary to describe the orientational order in binary mixtures in both uniaxial and biaxial nematic phases. For a single component, the model only requires one parameter, r₂, a ratio of anisotropic interaction strengths, to predict the temperature dependence of the four order parameters. The temperature dependence of the orientational distribution functions is illustrated for both rod-like and plate-like molecules. For binary mixtures, three anisotropic interaction strengths, r₁, r₂, and r₃, are needed to calculate the order parameters of both components as a function of concentration and temperature. The free energy is evaluated to predict the phase stability of the mixture. By systematically varying the anisotropic interaction strengths, temperature-concentration phase diagrams for a variety of molecular shapes are presented. The theoretical predictions suggest that binary mixtures of molecules with highly asymmetric shapes will display stable biaxial nematic phases.     

Effect of the surfactant alkyl chain length on the stabilisation of lyotropic nematic phases

Lyotropic quaternary mixtures of potassium alkanoates (KCx) and sodium alkyl sulphates (NaCxS), where x is the number of carbon atoms in their alkyl chains, were prepared to investigate the effect of the surfactant alkyl chain length on the stabilisation of lyotropic nematic phases. The lyotropic mixtures investigated were formed by the dissolution of KCx (NaCxS) surfactants in the mixture of Rb₂SO₄/1-decanol/water (Na₂SO₄/1-decanol/water), separately. The uniaxial-to-biaxial nematic phase transitions were identified from the temperature dependence of the birefringences of the nematic phases by means of laser conoscopy. The micelle dimensions were obtained from small-angle X-ray scattering measurements. It was observed that the increase in the surfactant alkyl chain length causes the micellar growth in the plane perpendicular to the main amphiphile bilayer. The surfactant alkyl chain length plays a key role on the shape anisotropy of micelles, which triggers the orientational fluctuations that are responsible for the stabilisation of the different lyotropic nematic phases.     

Chiral and orientationally ordered fluid mesophases formed by oxadiazole bisaniline based achiral bent mesogens

Development of new liquid crystalline materials exhibiting interesting properties and phases continues to be an enabling enterprise in the forward march of their successful display and non-display applications. The design and synthesis of a homologous series of liquid crystalline bent-core compounds derived from the oxadiazole bisaniline moiety and the phase behavior of three members of the series that exhibit nematic, smectic C, and dark conglomerate phases is reported. The liquid crystalline phases exhibited by these mesogens are characterized using polarized optical microscopy, differential scanning calorimetry and x-ray scattering techniques. All three homologs prepared exhibit the nematic phase. Interestingly, the homolog with short hexyl terminal chains exhibits only the nematic phase that is stable over a very broad, nearly 100 K wide, temperature range. The compound with terminal octyl chains shows the chiral dark conglomerate phase below the nematic phase despite the bent molecules being achiral. The homolog with dodecyl alkyl chains is found to possess the smectic-C and two additional lamellar phases besides the nematic phase. These compounds enrich the library of achiral bent-core materials capable of exhibiting chiral and nematic phases.     

The heat conductivity of liquid crystal phases of a soft ellipsoid string-fluid evaluated by molecular dynamics simulation

We have applied a nonequilibrium molecular dynamics heat flow algorithm to calculate the heat conductivity of a molecular model system, which forms uniaxial and biaxial nematic liquid crystals. The model system consists of a soft ellipsoid string-fluid where the ellipsoids interact according to a repulsive version of the Gay-Berne potential. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the discotic nematic phase, the heat conductivity has two components, one parallel and one perpendicular to the director, where the last mentioned component is the largest one. This order of magnitudes is reversed in the calamitic nematic phase. In the biaxial nematic phase there are three components of the heat conductivity, one in the direction around which the long axes of the molecules are oriented, this is the largest component, another one in the direction around which the normals of the broadsides of the molecules are oriented, this is the smallest component, and one in the direction perpendicular to these two directions with a magnitude in between those of the first mentioned components. The relative magnitudes of the components of the heat conductivity span a fairly wide interval so it should be possible to use the model to parameterise experimental data.     

Biaxial phase and coexistence of the two uniaxial nematic phases in the system sodium dodecyl sulphate–decanol–D2O

The system sodium dodecyl sulphate (SDS)/decanol (DeOH)/water presents, with temperature increase, an unusual phase transition between a stable biaxial phase and a coexistence region of the two uniaxial nematic phases (discotic N_D + cylindrical N_C). This has been detected previously by several methods for a sample with water/SDS molar ratio M_w = 36. Here, this system is investigated changing the ratio M_w to 32, where previously the coexistence region was reported after a discotic N_D phase, without the biaxial phase. We report now the existence of a biaxial N_B in the temperature range of ~2°C, defining for both values of M_w and the phase sequence as N_B – (N_D + N_C) – N_C. The change in temperature is followed by conoscopic and orthoscopic optical techniques and also analysed through the curve obtained by the technique of digital image processing of the textures, which reveals a continuous transition N_D – N_B – (N_D + N_C). While the biaxial phase is stable for at least 10 hours, in a reproducible way, the coexistence region evolves with time, and drops of the discotic phase grow immersed in a N_C matrix. Results are explained in terms of recent theories dealing with stabilisation of mixtures of cylinders and discs.     

A new soap/detergent/water lyotropic liquid crystal with a biaxial nematic phase

A new lyotropic liquid crystal, potassium laurate, decylammonium chloride and water, which has two uniaxial phases and a biaxial nematic phase, is reported. A surface of the phase diagram and X-ray diffraction studies are presented. The chemical stability of this mixture is compared with the potassium laurate/decanol/water mixture. Optical measurements of the birefringence and X-ray studies indicate that this new mixture is more stable than the usual mixtures with alcohol.     

A new soap/detergent/water lyotropic liquid crystal with a biaxial nematic phase

A new lyotropic liquid crystal, potassium laurate, decylammonium chloride and water, which has two uniaxial phases and a biaxial nematic phase, is reported. A surface of the phase diagram and X-ray diffraction studies are presented. The chemical stability of this mixture is compared with the potassium laurate/decanol/water mixture. Optical measurements of the birefringence and X-ray studies indicate that this new mixture is more stable than the usual mixtures with alcohol.