Elastic constants of uniaxial nematic liquid crystals of non-cylindrically symmetric molecules

We study in detail the influence of deviations from the molecular cylindrical symmetry on the fundamental elastic properties of uniaxial nematic liquid crystals. Results for the elastic constants are obtained for a range of molecular length-width ratio, temperature, density and molecular parameters. We compare calculated values with the experimental data of 8 OCB. It is observed that the effect of non-cylindrical molecular symmetry on the values of elastic constants of uniaxial of a nematic phase is small.     

Elastic constants of discotic (nematic) liquid crystals: effect of packing

Using a previously developed theory of nematic liquid crystals (Singh, Y., and Singh, K., 1986, Phys. Rev. A , 33, 3481) we present the calculation of elastic constants of discoticnematic liquid crystals and study the variation of elastic constants with packing fraction. The expressions for elastic moduli associated with 'splay', 'twist' and 'bend' modes of deformations are written in terms of order parameters characterizing the nature and amount of ordering in the phase and structural parameters. Numerical calculations are done for a model system, the molecules of which are hard oblate ellipsoids of revolution. It is observed that elastic constants are very sensitive to packing density and become larger with increase of shape anisotropy.     

Elastic constants,viscosity and dielectric properties of bent-core nematic liquid crystals doped with single-walled carbon nanotubes

Single-walled carbon nanotubes (SWCNTs) are dispersed in (4’-fluoro phenyl azo) phenyl-4-yl 3-[N-(4’-n-hecyloxy 2-hydroxybenzylidene)amino]-2-methylbenzoate (6–2M-F) a bent-core nematic (BCN) liquid crystalline medium composed of bent-shaped molecules with short core, reduced bend angle possessing polar fluoro substituent in longitudinal direction and methyl group in bent direction. Such molecules are at the borderline of typical bent-core and rod-like molecules resembling hockey stick shape with intermediate properties. The elastic anisotropy is negative for 6–2M-F (bend elastic constant K₃₃ < splay elastic constant K₁₁); similar to other BCNs reported earlier with smectic-like clusters; but turns to high positive (K₃₃ > K₁₁) value by insertion of SWCNT (concentration ≥0.05 wt.%) in 6–2 M-F. The ratio of K₃₃/K₁₁ becomes comparable to the calamitic liquid crystals (LCs) in doped system. Dielectric anisotropy increases in the nanocomposite implying enhanced nematic ordering due to π–π electron interaction between CNTs and the LC molecules. Threshold voltage at first increases and then decreases with increasing CNT concentration owing to the respective variations in splay viscosity of the system. The present study demonstrated the interaction of SWCNTs with BCN molecules and reveals significant modifications in viscoelastic, dielectric and ionic properties of the host.     

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.     

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.     

Elastic properties of bent-core nematic liquid crystals: the role of the bend angle

ABSTRACT

The nematic phase formed from bent-core liquid crystals has been the focus of intensive research for more than a decade. With the potential of biaxial nematic phase and other interesting features, such as high Kerr constants, large flexoelectric coefficients and anomalous elastic constants, these bent-core materials have been in the limelight of research. This paper presents a mini-review of the interesting elastic behaviour reported in various bent-core compounds. The review further focusses on two different types of bent-core compounds as exemplars: one derived from an oxadiazole and other a thiadiazole, highlighting the importance of bend angle in bent-core compounds. The universality of the unique behaviour of bend elastic constants via molecular field theory and atomistic modelling has also been summarised.     

Highly birefringent nematic and chiral nematic liquid crystals

We report a simple interference method to determine the dispersion of the extraordinary refractive index and birefringence of highly conjugated and coloured nematic liquid crystals used as light-emitting materials in organic electroluminescent devices. The measurements are made in the nematic glass phase at room temperature. The birefringence is highly dispersive and values up to 1.1 are obtained. Chiral groups are incorporated into the end chains giving a chiral nematic liquid crystal with a very wide stopband in the visible region. The Berreman matrix method is used to simulate transmission through the chiral nematic liquid crystal cell using the refractive index parameters obtained experimentally. Excellent agreement between theory and experiment is found.     

Highly birefringent nematic and chiral nematic liquid crystals

We report a simple interference method to determine the dispersion of the extraordinary refractive index and birefringence of highly conjugated and coloured nematic liquid crystals used as light‐emitting materials in organic electroluminescent devices. The measurements are made in the nematic glass phase at room temperature. The birefringence is highly dispersive and values up to 1.1 are obtained. Chiral groups are incorporated into the end chains giving a chiral nematic liquid crystal with a very wide stopband in the visible region. The Berreman matrix method is used to simulate transmission through the chiral nematic liquid crystal cell using the refractive index parameters obtained experimentally. Excellent agreement between theory and experiment is found.     

First-order transition between nematic phases in lyotropic liquid crystals

Experimental evidence for the existence of a first order transition between N_c-N_d uniaxial lyonematic phases as a function of the variable M_d (number of decanol molecules per amphiphilic molecule) is reported. The relevance of this evidence to molecular models for micellar aggregates is discussed. The evidence is for a change in micellar symmetry at this transition.     

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.     

New approximate formulae for the retardation factors of nematic liquid crystals with simple uniaxial anisotropy

Abstract

Simple formulae which yield a close approximation to the exact analytic solution for the longitudinal and transverse relaxation times T _|| and T _⊥ of the components of the dipole moment of a nematic liquid crystal with simple uniaxial anisotropy are presented. The new formula for T _|| yields a substantial correction to the Meier-Saupe formula [1966, Molec. Crystals, 1, 515]. It appears that both the longitudinal and transverse relaxation processes may be accurately described by a single Debye type relaxation mechanism with relaxation times T _|| and T _⊥.     

Elastic constants of nematic solutions of rod-like and semi-flexible polymers

Analytical expressions for the elastic constants of nematic polymer solutions are derived when the macromolecules are monodisperse rod-like, bidisperse rodlike or semi-flexible. These expressions are derived in the gaussian approximation so that they constitute exact leading terms of a general asymptotic expansion for high degree of nematic ordering although the results are justifiable only within the range of validity of the second virial approximation. The limiting forms are in complete agreement with recent numerical work for monodisperse rods.     

Elastic constants of nematic solutions of rod-like and semi-flexible polymers

Abstract

Analytical expressions for the elastic constants of nematic polymer solutions are derived when the macromolecules are monodisperse rod-like, bidisperse rodlike or semi-flexible. These expressions are derived in the gaussian approximation so that they constitute exact leading terms of a general asymptotic expansion for high degree of nematic ordering although the results are justifiable only within the range of validity of the second virial approximation. The limiting forms are in complete agreement with recent numerical work for monodisperse rods.     

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.     

Three homeotropically aligned nematic liquid crystals: comparison of ultrafast to slow time-scale dynamics

The dynamics of two nematic liquid crystals, 4-(trans-4(')-n-octylcyclohexyl)isothiocyanatobenzene and 4-(4-pentyl-cyclohexyl)-benzonitrile, are investigated as a function of temperature both in the homeotropically aligned nematic phase and in the isotropic phase using optical heterodyne-detected optical Kerr effect experiments, which measures the time derivative of the polarizability-polarizability-correlation function (orientational relaxation). Data are presented over a time range of 500 fs-70 micros for the nematic phase and 500 fs to a few hundred nanoseconds for the isotropic phase. The nematic dynamics are compared with a previously studied liquid crystal in the nematic phase. All three liquid crystals have very similar dynamics in the nematic phase that are very different from the isotropic phase. On the slowest time scale (20 ns-70 micros), a temperature-independent power law, the final power law, t(-f) with f approximately 0.5, is observed. On short time scales (approximately 3 ps to approximately 1 ns), a temperature-dependent intermediate power law is observed with an exponent that displays a linear dependence on the nematic order parameter. Between the intermediate power law and the final power law, there is a crossover region that has an inflection point. For times that are short compared to the intermediate power law (approximately <2 ps), the data decay much faster, and can be described as a third power law, although this functional form is not definitive. The isotopic phase data have the same features as found in previous studies of nematogens in the isotropic phase, i.e., the temperature-independent intermediate power law and von Schweidler power law at short to intermediate times, and a highly temperature-dependent long time exponential decay that is well described by the Landau-de Gennes theory. The results show that liquid-crystal dynamics in the nematic phase exhibit universal behavior.     

Spontaneous spreading of nematic liquid crystals

The spontaneous spreading of macroscopic drops of nematic liquid crystals on hydrophilic substrates has been investigated by interferometric techniques. There is a complex interplay between the elastic energy, due to antagonist anchoring at the interfaces, and the radial flow in the spreading drop. A relevant parameter appears to be the relative humidity of the atmosphere, because it controls the amount of water molecules adsorbed on the substrate and, therefore, the strength of anchoring defects. The spreading laws differ from the ones of simple wetting liquids, and contact line instabilities coupled to short- (anchoring) or large-scale (disclinations) defects of the nematic film are observed.     

Curvature and defects in nematic liquid crystals

ABSTRACT

The use of nematic liquid crystals for directed assembly of particles and for the creation of multistable systems depends on the ability to control the topological defects and the distortions of the director field. These are not only driven by topological constraints and by anchoring energies but also by the curvature field created by the bounding surfaces. This review explores the interaction between defects, topology, inclusions and curvature in nematics. I will introduce the relationship between curvature and the Frank elastic energy in nematics, and then I will give an overview of specific examples that show how this coupling can create unexpected behaviours, such as lock-and-key interactions, anchoring transitions on curved surfaces and memory effects.