Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ∂Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Abstract

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ?Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

Landau-de Gennes theory of the core structure of a screw dislocation in smectic A liquid crystals

We present details of calculations of the core structure of a screw dislocation in a smectic A liquid crystal, using the phenomenological Landau-de Gennes free energy functional. The order parameter frustration created by topological constraints far from the dislocation core is resolved in one of three qualitatively different ways. The three types of dislocation core solution are the DT (double twist), CL (classical), and BP (broken polar symmetry) solutions, respectively. The stability requirements for these structures are discussed, as a function of temperature, smectic elastic properties, and coupling between smectic and nematic order. The effect of possible inhomogeneity between left- and right-handed conformers is also examined.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

Molecular theory of smectic C liquid crystals

We generalize an earlier density functional theory of liquid crystals by Mederos and Sullivan. The original theory took account of anisotropic hard core interactions, and for suitable intermolecular interactions predicted nematic and smectic A phases as well as isotropic liquid and vapour phases. In this generalization we also take into account quadrupolar or dipole induced dipole interactions. The modified theory now also predicts the existence of a smectic C phase.     

Director fluctuations in inhomogeneously ordered nematic liquid crystals: An extension of elastic molecular field

In order to describe the order director fluctuations in nematic liquid crystalline systems with inhomogeneous order parameter, the approach based on Frank elastic theory is extended by introducing spatially dependent rotational viscosity and elastic constants. Using the proposed model, eigenmodes of director fluctuations in the vicinity of a disclination line of strength 1 are examined. Particular attention is paid to the behaviour of fluctuations in the vicinity of the structural transition in a cylindrical cavity.     

Some flow effects in continuum theory for smectic liquid crystals

This paper presents a constrained theory for smectic C liquid crystals that may be useful for the analysis of some effects in these materials. The theory is based on two simplifying assumptions, namely that the layers although deformed remain of constant thickness, and also that the tilt with respect to the layer normal remains fixed. The equilibrium version of the theory proves to be a non-linear generalization of the earlier Orsay theory, and promises to model a number of static effects satisfactorily. Here our aim is to examine preliminary predictions based on the corresponding dynamic theory, where some progress proves possible for shear flow, and also for a shear wave reflection-refraction experiment useful for the measurement of some viscous coefficients.     

Self-consistent field theory for lipid-based liquid crystals: hydrogen bonding effect

A model to describe the self-assembly properties of aqueous blends of nonionic lipids is developed in the framework of self-consistent field theory (SCFT). Thermally reversible hydrogen bonding between lipid heads and water turns out to be a key factor in describing the lyotropic and thermotropic phase behavior of such systems. Our model includes reversible hydrogen bonding imposed in the context of the grand canonical ensemble and exact conditions of binding equilibrium. The lipid molecules are modeled as a rigid head and a flexible Gaussian tail, and the water molecules are treated explicitly. Here, we focus on systems where the lipid molecule has a relatively small hydrophilic head compared to the hydrophobic tail, such as monoolein in water. Experimentally, this system has both normal phase sequences (inverted hexagonal to inverted double gyroid cubic phase) and reverse phase sequences (lamellar to inverted double gyroid cubic phase) as the water volume fraction increases. From SCFT simulations of the model, two phase diagrams corresponding to temperature independent or dependent interaction parameters chi are constructed, which qualitatively capture the phase behavior of the monoolein-water mixture. The lattice parameters of the simulated mesophases are compared with the experimental values and are found to be in semiquantitative agreement. The role of various structural and solution parameters on the phase diagrams is also discussed.     

Statistical mechanical theory for discotic liquid crystals Discotic nematic-isotropic transition properties

A statistical mechanical theory is applied to study the equilibrium properties of discotic nematic liquid crystals. We report the calculation of thermodynamic properties for a model system composed of molecules interacting through angle-dependent pair potentials which can be broken up into rapidly varying short-ranged repulsions and weak long-range attractions. The repulsive interaction is represented by a repulsion between hard oblate ellipsoids of revolution and is a short-range, rapidly-varying, potential. The influence of attractive potentials, represented by dispersion and quadrupole interactions on a variety of thermodynamic properties is analysed. It is found that the thermodynamic properties for the discotic nematic-isotropic transition are highly sensitive to the form of effective one-body orientational perturbation potential. The discontinuity in the transition properties is more pronounced in the case of quadrupole interaction than for anisotropic dispersion interaction. A remarkable symmetry in the transition properties between prolate ellipsoids (ordinary nematic) and oblate ellipsoids (discotic nematic) is observed.     

The development of theory for flow and dynamic effects for nematic liquid crystals

Today studies of flow phenomena in nematic systems normally employ the so-called Leslie-Ericksen theory. This theory was formulated in its present form in the 1960s, and it represents the culmination of theoretical developments that essentially started at the beginning of this century. This article gives an account of the evolution of the theory.     

Pyridinium salt liquid crystals Effect of mesogen extension and alkyl chain length

The thermotropism of 1-n-alkyl-(4-methyl and 4-tolyl)pyridinium bromides were compared for alkyl chain lengths ranging from n = 12 to 22 carbons. A smectic A mesophase is present in both series for the longer chain compounds, n ≥ 16, with the clearing temperature being similar for both series but increasing rapidly with chain length. The series with the elongated mesogen also possesses an ordered mesophase identified as smectic G. The transition between this mesophase and the S_A or isotropic phase in the 4-tolyl series, and the transition to and from the crystalline phase in both series, are affected relatively little by the alkyl chain length. It seems that the S_A mesophase is governed primarily by the amphiphilic character of the substances, whereas elongation of the ionic head group is responsible for the appearance of a more ordered mesophase at intermediate temperatures.     

Increased alignment of electronic polymers in liquid crystals via hydrogen bonding extension

Crucial for the development of enhanced electrooptic materials is the construction of highly anisotropic materials. Nematic liquid crystals are able to control the chain conformation and alignment of poly(phenylene ethynylene)s (PPEs), producing electronic polymers with chain-extended planar conformations for improved transport properties. Here, we show that the dichroic ratio, and hence polymer alignment, increases dramatically when interpolymer interactions are introduced by end capping the PPE with hydrogen bonding groups. This increased order can be readily turned off by the introduction of a competing monofunctionalized hydrogen bonding compound. The formation of hydrogen bonds between the polymers results in the formation of gels and elastomers which may be of interest for future applications.     

A molecular theory of pretransitional behaviour in smectogenic liquid crystals

The nature of the pretransitional behaviour in the isotropic phase prior to the formation of a liquid crystal mesophase depends critically on whether this is a nematic or a smectic A. The McMillan theory of the smectic A mesophase is used to provide a molecular theory of this difference in pretransitional behaviour.     

A simple theory of molecular organization in fullerene-containing liquid crystals

Systematic efforts to synthesize fullerene-containing liquid crystals have produced a variety of successful model compounds. We present a simple molecular theory, based on the interconverting shape approach [Vanakaras and Photinos, J. Mater. Chem. 15, 2002 (2005)], that relates the self-organization observed in these systems to their molecular structure. The interactions are modeled by dividing each molecule into a number of submolecular blocks to which specific interactions are assigned. Three types of blocks are introduced, corresponding to fullerene units, mesogenic units, and nonmesogenic linkage units. The blocks are constrained to move on a cubic three-dimensional lattice and molecular flexibility is allowed by retaining a number of representative conformations within the block representation of the molecule. Calculations are presented for a variety of molecular architectures including twin mesogenic branch monoadducts of C60, twin dendromesogenic branch monoadducts, and conical (badminton shuttlecock) multiadducts of C60. The dependence of the phase diagrams on the interaction parameters is explored. In spite of its many simplifications and the minimal molecular modeling used (three types of chemically distinct submolecular blocks with only repulsive interactions), the theory accounts remarkably well for the phase behavior of these systems.     

Transfer-matrix theory of the crystal–columnar transition in polymeric liquid crystals

The statistical–mechanical problem of the transition between crystalline and columnar phases in a main-chain liquid–crystalline polymer is treated in a simple model in which only longitudinal motions of the polymer chains are permitted. A mean-field approximation for the interchain potential is used to obtain a self-consistent equation for the crystalcolumnar transition temperature. When applied to typical homopolymers this theory correctly predicts transition temperatures above the degradation temperature; when applied to a crude model of a random copolymer a temperature in the observed range is predicted.     

Phenomenological theory of the nematic to lamellar phase transition in lyotropic liquid crystals

A phenomenological theory is presented to describe the nematic to lamellar phase transition in lyotropic liquid crystals. The problem of the first or second order transition is explored by means of the variation of the surfactant concentration. The possibility of the tricritical point at the nematic to lamellar phase transition is discussed in a phenomenological way. The influence of the electrolyte on this transition is also discussed by varying the coupling between the electrolyte concentration variables and the order parameters. The theoretical prediction is found to be in good qualitative agreement with experimental results.