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 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 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.     

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.     

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.     

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.     

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.     

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.     

Structural and dynamical analysis of monodisperse and polydisperse colloidal systems

We present a semigrand ensemble Monte Carlo and Brownian dynamics simulation study of structural and dynamical properties of polydisperse soft spheres interacting via purely repulsive power-law potentials with a varying degree of "softness." Comparisons focus on crystal and amorphous phases at their coexistence points. It is shown through detailed structural analysis that as potential interactions soften, the "quality of crystallinity" of both monodisperse and polydisperse systems deteriorates. In general, polydisperse crystalline phases are characterized by a more ordered structure than the corresponding monodisperse ones (i.e., for the same potential softness). This counter-intuitive feature originates partly from the fact that particles of different sizes may be accommodated more flexibly in a crystal structure and from the reality that coexistence (osmotic) pressure is substantially higher for polydisperse systems. These trends diminish for softer potentials. Potential softness eventually produces substitutionally disordered crystals. However, substitutional order is apparent for the hard-spherelike interactions. Diffusionwise, crystals appear quite robust with a slight difference in the vibrational amplitudes of small and large particles. This difference, again, diminishes with potential softness. Overcrowding in amorphous polydisperse suspensions causes "delayed" diffusion at intermediate times.     

Vanadium pentoxide gels: From “chimie douce” to “matière molle”

This article presents a review of the colloidal and liquid-crystalline properties of vanadium pentoxide suspensions from a physicist's perspective. The processes occurring during the synthesis of these suspensions are first discussed. Then, the liquid-crystalline properties of V₂O₅ sols and gels are described. These nematic phases are easily aligned by weak magnetic fields or by alternative electric fields. The delicate interplay between repulsive hardcore and electrostatic interactions and van der Waals attractions defines the (concentration, ionic strength) phase diagram that includes an isotropic phase, a uniaxial nematic phase, a biaxial nematic gel state and a flocculated state. Deuterium NMR spectroscopy of D₂O molecules gives information on the rotational dynamics of the nematic phase. Finally, various applications of these colloidal suspensions in the fields of hybrid organic/inorganic materials, mesoporous solids, and of the structures of biomolecules, are reviewed.     

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.     

Bimodal form distribution from modelling biaxial lyotropic liquid crystal solutions through a polydisperse Maier–Saupe model

Biaxial nematic phases have been the subject of a long list of studies. In particular, they were found for a few lyotropic micellar solutions. There is a debate in the literature on whether the micellar aggregates should be biaxial, or if biaxiality could be the result of perpendicular alignment of uniaxial particles of cylinder-like and disc-like geometry in a mixture. Based on recent studies on the phase stability of such mixtures, we have investigated a polydisperse distribution of uniaxial particles interacting through a Maier–Saupe potential. Our calculations were developed for a general distribution of micellar anisometries. The distribution was obtained from the fitting of our results to the experimental data of Yu and Saupe’s well-known 1980 paper, near the Landau point, yielding a bimodal distribution, with the presence of two quadrupoles referred to objects of opposite symmetry, that is to prolate and oblate micelles. This result lends support to the rationalization of the biaxial phase for lyotropic systems in terms of a polydisperse mixture of rod-like and disc-like micelles.     

Phase biaxiality in nematic liquid crystalline side-chain polymers of various chemical constitutions

In a previous deuterium NMR study conducted on a liquid crystalline (LC) polymer with laterally attached book-shaped molecules as the mesogenic moiety, we have revealed a biaxial nematic phase below the conventional uniaxial nematic phase (Phys. Rev. Lett. 2004, 92, 125501). To elucidate details of its formation, we here report on deuterium NMR experiments that have been conducted on different types of LC side-chain polymers as well as on mixtures with low-molar-mass mesogens. Different parameters that affect the formation of a biaxial nematic phase, such as the geometry of the attachment, the spacer length between the polymer backbone and the mesogenic unit, as well as the polymer dynamics, were investigated. Surprisingly, also polymers with terminally attached mesogens (end-on polymers) are capable of forming biaxial nematic phases if the flexible spacer is short and thus retains a coupling between the polymer backbone and the LC phase. Furthermore, the most important parameter for the formation of a biaxial nematic phase is the dynamics of the polymer backbone, as the addition of a small percentage of low molar mass LC to the biaxial nematic polymer from the original study served to shift both the glass transition and the appearance of detectable biaxiality in a very similar fashion. Plotting different parameters for the investigated systems as a function of T/Tg also reveals the crucial role of the dynamics of the polymer backbone and hence the glass transition.     

Computer simulation studies of anisotropic systems XXIX. Quadrupolar Gay-Berne discs and chemically induced liquid crystal phases

Liquid crystal phases can be induced chemically by mixing compounds whose specific interactions are such that the transition temperature for the induced phase is higher than the melting points of the two compounds. A particularly dramatic example of such behaviour is the creation of a columnar nematic and a hexagonal columnar phase on mixing discotic multiynes with 2,4,7-trinitrofluorenone. Although the intense colour of the mixture indicates a strong charge-transfer band, it is uncertain as to whether the charge-transfer interaction between unlike molecules is enough to stabilize the induced liquid crystal phases. An alternative explanation for the formation of such phases involves an electrostatic quadrupolar interaction between the components,whose quadrupole moments differ in sign. This interaction weakens the face-to-face attraction for like particles while strengthening it for unlike particles. We have explored this possible explanation for chemically induced liquid crystal phases in discotic systems by modelling the basic interaction between discs with a Gay-Berne potential, to which is added a point quadrupolar interaction. We have determined the phase behaviour of the pure systems and their binary mixtures with constant pressure Monte Carlo simulations. It would seem that the quadrupolar interaction can account for many of the features of chemically induced liquid crystals.     

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.     

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.     

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.