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.     

Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.     

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.     

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.     

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.     

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes σ(1) > σ(2) > σ(3). A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio κ(1) = σ(1)/σ(2) while keeping κ(2) = σ(2)/σ(3), we predict phase diagrams for various values of κ(2) which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid types are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for κ(2)? 2.5. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxiality centred at κ(1)≈κ(2) which widens as κ(2) increases. For κ(2)? 5 the region κ(2)≈κ(1) of the packing-fraction vs. κ(1) phase diagrams exhibits interesting topologies which change qualitatively with κ(2). We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric in the neighbourhood of κ(1)≈κ(2) is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.     

Computer simulation studies of anisotropic systems. XXII. An equimolar mixture of rods and discs: A biaxial nematic?

In principle, binary mixtures of rod-like and disc-like particles should exhibit a biaxial nematic phase, but in practice phase separation into two uniaxial nematic phases prevents this. Here, we report the results of a computer simulation study of an equimolar mixture of rods and discs in which phase separation is not allowed. The particles are confined to the sites of a simple cubic lattice in which each rod is surrounded by six discs and vice versa. Neighbouring particles interact such that they prefer to align with their respective symmetry axes orthogonal to each other. In contrast, the interaction between next nearest neighbours, which are either rods or discs, is such that their symmetry axes tend to be parallel. Monte Carlo simulations of this model mixture show that an orientationally ordered phase exists at low temperatures. This nematic phase has overall uniaxial symmetry and the particles have a negative second rank orientational order parameter, indicating that they tend to align at right angles to the director. The two interpenetrating sub-lattices containing either rods or discs, however, exhibit a biaxial nematic phase. The results of the simulation are found to be in reasonable agreement with the predictions of a molecular field theory for this model mixture. We have also investigated the behaviour of this mixture when the rods and discs are allowed to exchange between their lattice sites. The mixture is found to separate into two uniaxial nematic phases composed essentially of either rods or discs, as expected.     

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.     

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.     

Bifurcational analysis of the isotropic-nematic phase transition of rigid rod polymers subjected to biaxial stretching flow

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non-equlibrium isotropic-nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic-biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15 , 1272 (1982)], which are based on a version of the Onsager theory of isotropic-nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.     

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.     

Orientation of a chiral smectic C elastomer by mechanical fields

It is well known that, with respect to the director, nematic elastomers can be macroscopically aligned by uniaxial mechanical fields. Extending this method to a chiral smectic C elastomer, depending on the experimental set-up either smectic layer orientation or director orientation parallel to the stress axis occurs. In order to align the director and the smectic layers a biaxial mechanical field (e.g. shear field) consistent with the phase symmetry has to be used to achieve a macroscopically uniform orientation of the untwisted smectic C^* structure.     

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.     

Influence of the smectic A-nematic transitional order on the formation of the smectic phases of 4-n-hexyloxybenzylidene-4′-n-butyIaniline and 4-n-butyloxybenzylidene-4′-n-octyIaniline from an electrically deformed nematic phase

Abstract

The crucial role of the smectic A-nematic transitional order for the formation of the smectic A, B and G phases from an electrically deformed nematic phase of the liquid crystal 4-n-hexyloxy-benzylidene-4′-n-butylaniline (6O.4) with a typical smectic A-nematic first order transition and the formation of the smectic A and B phases from an electrically deformed nematic phase of the liquid crystal (4-n-butyloxy-benzylidene-4′-n-octylaniline (40.8) with a smectic A-nematic second order transition has been demonstrated. The nematic phase was deformed by an AC voltage of 2U,_th 5U _th and 10U _th, where U _th is the threshold voltage which causes the appearance of the Fréedericksz transition in the homeotropic nematic layer. The smectic textures have been observed on free cooling of the nematic phase or after the use of an oven. The smectic A phase of the liquid crystal 60.4 was observed with the formation of a clear smectic A-nematic phase boundary while the smectic A phase of the liquid crystal 40.8 has been formed from intermediate pretransitional stripes, observed by Cladis and Torza [1]. The homeotropic anchoring of the direction was crucial for the formation of the smectic phases of the liquid crystal 40.8 but not significant for the liquid crystal 60.4.     

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.     

New liquid crystalline phases with layerlike organization

Novel lamellar mesophases which are quite distinct from conventional smectic mesophases were obtained with a bolaamphiphilic triblock molecule composed of a rigid biphenyl core, two polar 2,3-dihydroxypropoxy groups in the terminal 4- and 4'-positions, and a semiperfluorinated chain [O(CH2)6C10F21] in the lateral 3-position. The competitive combination of microsegregation and rigidity in this molecule leads to layer structures in which the bolaamphiphilic cores segregate from the lateral chains into distinct sublayers. In these sublayers the biphenyl cores are aligned parallel to the layer planes. Decreasing the temperature leads to a subsequent inset of orientational and positional order of the biphenyl unit, which leads to a transition from an uniaxial SmA phase to a biaxial SmAb phase and finally to a mesophase with an additional periodicity within the aromatic sublayers. Here, microsegregation occurs on two distinct levels: The segregation of the nonpolar chains from the aromatic cores leads to the "bulk" layer structure and segregation of polar and aromatic subunits within the aromatic sublayers gives rise to an additional periodicity within the aromatic sublayers. These phases can be regarded as smectic phases built up by quasi-2D layers with nematic, respectively SmA-like order, separated by isotropic layers of the lateral chains.     

Effect of the presence of strong and weak electrolytes on the existence of uniaxial and biaxial nematic phases in lyotropic mixtures

The lyotropic mixture of potassium laurate/decanol/water presenting only the uniaxial nematic calamitic phase was doped with one strong (potassium chloride, KCl) and 11 weak electrolytes with phenyl-rings (DL-mandelic acid, benzoic acid, DL-phenyllactic acid, phenylacetic acid, phenol and phenylmethanol) and with cyclohexyl-ring (RS-hexahydromandelic acid, cyclohexanecarboxylic acid, cyclohexaneacetic acid, cyclohexanol and cyclohexylmethanol), separately. We also chose two nonpolar dopant molecules, benzene and cyclohexane, for the comparison of them with weak electrolytes, since they are located in the hydrocarbon core of the micelle. The nematic phase sequences, in particular the presence of the biaxial nematic phase, were investigated as a function of the dopant molar concentration and temperature. The laser conoscopy and small-angle X-ray scattering techniques were used to characterise the different nematic phases. Weak electrolytes having –COOH group as polar part were found to be very effective in stabilising the three nematic phases (two uniaxial and a biaxial). Guest molecules with only the –OH group did not show any effect on the stabilisation of other nematic phases. The experimental results are interpreted considering the screening effect of the hydrophilic parts of the dopants on the repulsion between the polar heads of the main amphiphilic molecules at micelle surfaces. This process favours the increase of the more flat micellar surfaces of micelles, which triggers the orientational fluctuations responsible for the biaxial and discotic nematic phases.     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.     

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.     

Uniform Alignment of Chiral Smectic C Elastomers Induced by Mechanical Shear Field

Up to now, liquid crystalline elastomers have been strenuously studied to obtain high orientation induced by mechanical fields. It is known that a uniaxial mechanical field is sufficient to obtain macroscopically uniform alignment for nematic and smectic A liquid crystalline elastomers having uniaxial symmetry. Here the orientation mechanism of biaxial smectic C* elastomers in mechanical shear fields has been investigated. A significant influence of a shear field on the orientation of the smectic C* elastomer is confirmed. In addition, we succeeded in obtaining a monodomain sample of the smectic C* elastomer by this process.