Effect of the temperature range of the nematic phase on the induction of a twist grain boundary phase in non-chiral liquid crystals

Recent experimental results suggest that the twist grain boundary phase may be induced in non-chiral smectic liquid crystals by confining the material in a twist cell in which the nematic directors at the two surfaces are perpendicular to each other. However, the effect of the temperature range of the nematic phase on the induction of the twist grain boundary (TGB) phase has not been studied to date. We have performed experiments on non-chiral liquid crystals having the nematic-smectic A (N-SmA) phase transition sequence and confined in a twist cell. It is observed that materials with a second order N-SmA phase transition show characteristics of a TGB phase, but a material with a first order N-SmA transition does not.     

Effect of the temperature range of the nematic phase on the induction of a twist grain boundary phase in non-chiral liquid crystals

Recent experimental results suggest that the twist grain boundary phase may be induced in non-chiral smectic liquid crystals by confining the material in a twist cell in which the nematic directors at the two surfaces are perpendicular to each other. However, the effect of the temperature range of the nematic phase on the induction of the twist grain boundary (TGB) phase has not been studied to date. We have performed experiments on non-chiral liquid crystals having the nematic-smectic A (N-SmA) phase transition sequence and confined in a twist cell. It is observed that materials with a second order N-SmA phase transition show characteristics of a TGB phase, but a material with a first order N-SmA transition does not.     

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.     

Theory of nematic–smectic phase separation in thin twisted liquid crystal cells

Recently it has been shown experimentally by the authors that a highly twisted thin nematic cell at low temperatures can separate into a smectic A region in the middle of the cell surrounded by twisted nematic layers at the boundaries. In this case the twist is expelled into the nematic layers and the nematic–smectic A transition temperature is strongly depressed. We present a thermodynamic theory of such a phase transition in a twisted nematic cell, taking into account that the smectic A slab inside the nematic cell can be stable only if the decrease of free energy in the smectic region overcomes the increase in distortion energy of the twist deformation in the nematic layers plus the energy of the nematic–smectic A interface. In such a system the equilibrium thickness of the smectic A slab corresponds to the minimum of the total free energy of the whole cell, which includes all the bulk and surface contributions. Existing experimental data are at least qualitatively explained by the results of the present theory. This opens a unique possibility to study the properties of the nematic–smectic interface which is perpendicular to the smectic layers.     

2H NMR measurements of the molecular orientational ordering in a reentrant liquid-crystalline mixture

Deuterium NMR measurements of the molecular orientational ordering (nematic order) are reported for a reentrant binary mixture of some alkoxy-eyanobiphenyls (nOCB) to which small amounts of perdeuterated p-xylene have been added. The results indicate that the degree of orientational order is enhanced at the smectic A to reentrant nematic phase transition. This effect is shown to be in agreement with the predictions of a Landau-type theory of the reentrant phase transition where-by this phase transition is explained as the result of a coupling between the smectic and the nematic order parameters.     

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.     

Glass formation in the Gay-Berne nematic liquid crystal

We present the results of molecular dynamics simulations of the Gay-Berne model of liquid crystals, supercooled from the nematic phase at constant pressure. We find a glass transition to a metastable phase with nematic order and frozen translational and orientational degrees of freedom. For fast quench rates the local structure is nematic-like, while for slower quench rates smectic order is present as well.     

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.     

Theory of nematic-smectic phase separation in thin twisted liquid crystal cells

Recently it has been shown experimentally by the authors that a highly twisted thin nematic cell at low temperatures can separate into a smectic A region in the middle of the cell surrounded by twisted nematic layers at the boundaries. In this case the twist is expelled into the nematic layers and the nematic-smectic A transition temperature is strongly depressed. We present a thermodynamic theory of such a phase transition in a twisted nematic cell, taking into account that the smectic A slab inside the nematic cell can be stable only if the decrease of free energy in the smectic region overcomes the increase in distortion energy of the twist deformation in the nematic layers plus the energy of the nematic-smectic A interface. In such a system the equilibrium thickness of the smectic A slab corresponds to the minimum of the total free energy of the whole cell, which includes all the bulk and surface contributions. Existing experimental data are at least qualitatively explained by the results of the present theory. This opens a unique possibility to study the properties of the nematic-smectic interface which is perpendicular to the smectic layers.     

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.     

Twist viscosities and flow alignment of biaxial nematic liquid crystal phases of a soft ellipsoid-string fluid studied by molecular dynamics simulation

We have calculated the twist viscosity and the alignment angle between the director and the stream lines in shear flow of a liquid crystal model system, which forms biaxial nematic liquid crystals, as functions of the density, from the Green-Kubo relations by equilibrium molecular dynamics simulation and by a nonequilibrium molecular dynamics algorithm, where a torque conjugate to the director angular velocity is applied to rotate the director. The model system consists of a soft ellipsoid-string fluid where the ellipsoids interact according a repulsive version of the Gay-Berne potential. Four different length-to-width-to-breadth ratios have been studied. 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 uniaxial nematic phase there is one twist viscosity and one alignment angle. In the biaxial nematic phase there are three twist viscosities and three alignment angles corresponding to the rotation around the various directors and the different alignments of the directors relative to the stream lines, respectively. It is found that the smallest twist viscosity arises by rotation around the director formed by the long axes, the second smallest one arises by rotation around the director formed by the normals of the broadsides, and the largest one by rotation around the remaining director. The first twist viscosity is rather independent of the density whereas the last two ones increase strongly with density. One finds that there is one stable director alignment relative to the streamlines, namely where the director formed by the long axes is almost parallel to the stream lines and where the director formed by the normals of the broadsides is almost parallel to the shear plane. The relative magnitudes of the components of the twist viscosities span a fairly wide interval so this model should be useful for parameterisation experimental data.     

Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

ABSTRACT

It is generally accepted that the transition into the twist–bend nematic phase (N_TB) is driven by an elastic instability related to the reduction of the bend elastic constant. Here we use a molecular–statistical theory to show that sufficiently strong polar interactions between bent-shaped molecules may lead to experimentally observed reduction of the bend elastic constant in the nematic phase even if electrostatic dipole–dipole interactions are not taken into account. We propose a simple model of bent–core particles and derive explicit analytical expressions which enable one to understand how polar molecular shape affects the elastic constants, and, in particular, the important role of the bend angle. Numerical graphs showing temperature variations of all elastic constants are also presented including the variation of the bend and splay elastic constants before and after the renormalisation determined by local polar order of molecular steric dipoles and the corresponding polar correction to the one-particle distribution function.     

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.     

The orientational order parameters of a dendritic liquid crystal organo-siloxane tetrapode oligomer, determined using polarized infrared spectroscopy

The observed macroscopic anisotropic properties such as the components of infrared (IR) absorbances of liquid crystals are expressed in terms of the order parameters of the long molecular axis, molecular, and phase biaxiality. The order parameters of the organo-siloxane tetrapode liquid crystal of zero dendritic order (G0) in its nematic and smectic phases have been determined using results of the polarized IR spectroscopic measurements on a planar homogenously and hometropic aligned cells. The spatial components of the absorbances for the vibrational bands (in the mesogenic unit, terminal chains, and spacer) have been measured and analyzed. For the laboratory reference system, the apparent orientational order parameter S of the mesogen unit shows a significant drop in the transition from the nematic to the smectic phase while the phase biaxiality order parameter P increases to almost 0.4 in the smectic phase. This result shows that the director is tilted out of the sample plane in the smectic phase. The molecular biaxiality parameter D is found to be positive both for the nematic and smectic phases. This suggests that the carbonyl dipoles are oriented close to the tilt plane. For the vibrational bands in the chains, low values of S and D indicative of their low orientational order are obtained. As a result of the interaction among the molecules in the tilted smectic phases, the transition dipoles show positive correlations for the transversal and negative for the longitudinal dipoles.     

Experimental study of the director pattern dynamics in the vicinity of the Fréedericksz twist geometry

We present an experimental study of the transient periodic structures appearing in the nematic director field in the magnetically induced reorientation of the director in the vicinity of the twist Fréedericksz geometry. Thin nematic samples (50?µm thick) were exposed to magnetic fields of variable intensity and orientation relative to the surface aligning direction of the sample. The director reorientation was induced by a rapid rotation of the sample in the static magnetic field producing a misalignment between the director and the magnetic field. The director field was optically monitored during the reorientation process and the transient periodic structures were characterized. Two types of periodic structures could be identified, namely bands and walls. Walls grow from bands close to the twist Fréedericksz geometry. The time dependence of the wave length and inclination of the periodic structures was obtained as a function of the magnetic field intensity and orientation relative to the surface aligning direction of the sample. The results for the bands are compared with the predictions of a model that we specifically developed to account for the non-orthogonal field orientations. It is seen that our model can account rather well for the experimental results considering that it uses only the field rotation time as adjustable parameter. All other model parameters are known.     

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.     

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.     

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.     

Multiple Polar and Non-polar Nematic Phases

Liquid-crystal materials exhibiting up to three nematic phases are reported. Dielectric response measurements show that while the lower temperature nematic phase has ferroelectric order and the highest temperature nematic phase is apolar, the intermediate phase has local antiferroelectric order. The modification of the molecular structure by increasing the number of lateral fluorine substituents leads to one of the materials showing a direct isotropic-ferronematic phase transition.