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.     

Structural and dynamic properties of a new type of discotic nematic compounds

Thermodynamic, structural and dynamical properties of a new type of discotic compounds, a hydrocarbon without any heteroatoms, displaying a nematic discotic phase have been investigated by means of X-ray diffraction, electro-optical relaxation, and calorimetric studies. Of particular interest are the strength of the first order nematic—isotropic phase transition and the nature of the orientational fluctuations in the isotropic phase. The short range positional order was found to be biaxial in both the isotropic and the nematic phase. The isotropic phase displays strong pretransitional effects originating from orientational fluctuations in the neighbourhood of the transition to the nematic phase. The character of these pretransitional effects differs from that found for calamitic systems in that the number of correlated molecules g₂ is extremely large, of the order of 600 at the clearing temperature and the electro-optical relaxation time is very large, caused by the large value of g₂.     

Order parameter of side groups of a polysiloxane in liquid crystalline uniaxial phases

The orientational order of a liquid crystalline side chain polysiloxane has been investigated by means of polarized light spectroscopy and dielectric relaxation measurements. The order parameters (P₂) and (P₄) have been determined as a function of the temperature for the smectic and nematic phases. The orienting properties of the polysiloxane investigated have been compared with those of a polysiloxane with the same mesogenic groups, but a shorter spacer.     

Solute-Solvent Interactions in the Nematic and Smectic A Phases of 4 4-di-n-Heptylazoxybenzene Studied by Deuteron NMR

The orientational order parameters have been measured by deuteron N.M.R. of both solute (at low dilution) and solvent in various binary mixtures involving the liquid crystal 4,4'-di-n-heptylazoxybenzene (HAB). The solutes studied were azoxybenzene-d₁₀ and n-heptylbenzene-d₇ which are fragments of HAB, azobenzene-d₁₀ because of its similarity to azoxybenzene, and anthracene-d₁₀ because of its known structure and symmetric shape. The major and biaxial order parameters of the solutes are analysed in terms of a molecular field model for the potential of mean torque for biaxial particles. The behaviour of the solute order parameters on approaching and entering the smectic A phase is interpreted in terms of a temperature and phase dependent partitioning of the solute between aromatic and aliphatic regions of the solvent.     

Non-monotonic temperature dependence of the alignment of a nematic mixture on a ferroelectric substrate

Polarization optic techniques have been applied to study specific features of the anisotropic interaction between a dye-doped eutectic mixture of nematic liquid crystals p-methoxybenzylidene-p-n-butylaniline and p-ethoxybenzylidene-p-n-butylaniline and a polar surface of a ferroelectric triglycine sulphate crystal over the temperature range including the substrate Curie point T _c. It has been found that the temperature-induced structural changes in the nematic layer in the vicinity of T _c are related to the changes in the orientational part of the tensor order parameter Q_ik . The temperature dependence of the director angle θ¯, averaged over the nematic layer, has been obtained from the effective dichroism values of solute absorption. The experimental data were interpreted using the model, in which the anisotropic part of the surface energy has two terms with orthogonal easy axes.     

2H-N.M.R. studies of flexibility and orientational order in nematic liquid crystals

Deuteron magnetic resonance spectroscopy (²H-N.M.R.) has been used to investigate the effect of the nematic environment on the flexibility and orientational order of two perdeuteriated cyanobiphenyl homologues: 4-methyl-4'-cyanobiphenyl (1CB-d₁₁) and 4-n-pentyl-4'-cyanobiphenyl (5CB-d₁₉). The systems studied were low concentrations of 1CB-d₁₁ and 5CB-d₁₉ dissolved in the nematic phases of 5CB, N-(-4-ethoxybenzylidene)-4'-n-butylaniline (EBBA), Merck ZLI-1132 (1132) and a 55wt% mixture of 1132: EBBA. The spectra are dramatically different in these environments. Previous studies on small solutes have suggested that in the 55wt% 1132: EBBA mixture (at 301.4 K) the dominant orienting mechanism depends on the size and shape of the molecule which suggests that it is a short range repulsive interaction. This interaction has been modelled by treating the liquid crystal as an elastic continuum and the solute as a collection of van der Waals spheres which stretch the liquid crystal in the two dimensions perpendicular to the director. The distortion of the liquid crystal depends on the dimensions of the solute, and the elastic energy is described in terms of a Hooke's law force constant, k. The model is extended to include flexible liquid crystal molecules and quadrupolar couplings are calculated for each conformation of the 5CB chain. Statistical averaging over all conformations gives an excellent fit to the experimental spectrum. The results for 1CB and 5CB show that in the other nematic phases contributions from additional mechanisms must be included. Previous studies of ²H₂ and other solutes indicate that the additional mechanism is the interaction between the solute molecular quadrupole moment and the mean electric field gradient of the liquid crystal.     

X-ray study of the nematic and smectic A phases of the cyano-substituted pyridines

We report an X-ray study of lamellar ordering in the nematic and smectic A phases of a homologous series of polar liquid crystals, the 2-(4-alkylphenyl)-5-cyanopyridines (nCP). Experiments were carried out using a diffractometer with a linear position sensitive detector. In the nematic and smectic A phases of the nCP and their mixtures with non-polar 4-n-butyl-4'-methoxyazoxybenzene two types of layering were found. One corresponds to the fluctuations of the smectic density wave with a monolayer wavevector q₁, and the other is due to the partial bilayer fluctuations with the incommensurate wavevector q₂ ≠ q₁/2. The temperature dependences of the X-ray scattering intensity and the longitudinal correlation length for both types of layering in the nematic phase are presented. The critical behaviour in the vicinity of the smectic A-nematic phase transition occurs for a fluctuation mode, either q₁ or q₂, depending on the position on the liquid crystal phase diagram. The influence of the molecular structure of cyano-substituted pyridines on the formation of layered structures of different types is also discussed.     

First order transitions to a lyotropic biaxial nematic

The phase diagram of the sodium dodecylsulphate/decanol/water system is studied by²H NMR spectroscopy in the range between the calamitic nematic (N⁺_C) and discotic nematic (N^-_D) phases. In this narrow range a nematic biaxial phase (N_BX) is observed. The phase transitions between the nematic phases are all of first order. The shape of the surfactant aggregates in the nematic phases varies with composition and temperature.     

N.M.R. study of segmental molecular interactions in liquid crystals

A simple statistical model of interacting non-rigid molecules, based on a perturbation expansion of the pair correlation function and the additivity of segmental interactions, is applied to the study of orientational order as measured by N.M.R. in the nematic and S_A phases of 4-n-alkyl-4'-cyanobiphenyls (N-CB, N = 5 to 8), the nematic and S_C phases of 4-n-alkyloxybenzoic acids (N-OBA, N = 7, 8) and the D_h0 columnar discotic phase of hexa-alkyloxytriphenylenes (N-THE, N = 5 to 8). The order parameters of each homologous series are correctly described in terms of two isotropic and two anisotropic segmental coupling constants. The model predicts certain relations among coupling constants pertaining to different homogous series. These predictions are supported by the results obtained for the three types of compounds studied.     

An investigation of solute-liquid crystal interaction in hydrogen bonded complexes of palmitic acid and p-octyloxybenzoic acid

The orientational order of a liquid crystalline phase which has a specific solute-liquid crystal interaction was investigated using nuclear magnetic resonance. Three isotopically substituted species of palmitic acid (palmitic acid-d₃₁, 1-¹³C-2.2-H₂-palmitic acid-d₂₉ and 2,2,3,3-H₄-palmitic acid-d₂₇) were dissolved in the liquid crystal p-octyloxybenzoic acid (p-OOBA) and the proton, deuteron and carbon 13 NMR spectra recorded as a function of temperature. ¹H-¹³H dipolar couplings were observed using a spin echo pulse sequence which removes heteronuclear dipolar couplings to the chain deuterons. In the case of the carbon 13 labelled compound, ¹H-¹³C dipolar couplings could be observed by applying an additional refocusing pulse to the ¹³C spins. The dipolar and quadrupolar couplings were used to calculate the complete orientational order matrix of the alpha methylene segment of palmitic acid in p-OOBA. The liquid crystal was shown to largely determine the orientational order of the head group and this was attributed to intermolecular hydrogen bonding. The dipolar and quadrupolar couplings for the rest of the chain were interpreted in terms of a mean field equilibrium statistical model, based on the Samulski Inertial Frame Model. Hydrogen bonding was shown to be of greater importance in the orientational ordering of the solutes in the liquid crystal than are electrostatic interactions in the ordering of the amphiphile in the potassium palmitate/water system.     

Solute alignment in liquid crystal solvents The Saupe ordering matrix for perylene and pyrene

The complete second rank ordering matrix for perylene-d₁₂ and pyrene-d₁₀ in four different thermotropic liquid crystals has been determined over large temperature ranges, by interpreting the quadrupolar splittings observed from the deuterium N.M.R. spectra. The dipolar couplings also observed in the spectra were determined by computer simulation for both probes, allowing the commonly made assumptions of rigidity and planarity of these molecules to be tested. It is found that the perylene results are consistent with a non-rigid and non-planar structure with an average twist angle between the napthtalene units of 11.6°, whereas pyrene is rigid and planar within experimental error. It is also observed that both molecules are highly biaxial in their orientational behaviour and therefore another assumption often made especially in fluorescence measurements, that of disc-like cylindrical symmetry, is invalid. The results are interpreted in terms of a molecular field theory which predicts the variation of (S_xx - S_yy) with S_zz by calculating these quantities from the potential of mean torque, U(β, γ), of rigid solutes, expressed solely in terms of one adjustable parameter, the biaxiality parameter, λ. This parameter is predicted by some theories to be both temperature and solvent independent, but our results show that there is a weak temperature dependence and a stronger solvent dependence.     

Thermodynamic characterization of ternary solutions of uncharged polymers

The thermodynamic interactions in aqueous solutions of uncharged polymers were studied. Using a gel-deswelling method, the water activities (chemical potentials) in binary and ternary (two polymers in one solvent) solutions of methylcellulose (MC), polyvinyl alcohol (PVA) and polyvinyl pirrolidone (PVP), respectively were determined at various polymer volume fractions (1.0 × 10⁻² < v₂ < 1.0 × 10⁻¹). On the theoretical basis of the Flory–Huggins approximations, the relevant solvent–segment (χ₁₂ or χ₁₃) and segment–segment pair interaction parameters (χ₂₃) have been calculated.

The solvent activity curves (ln a₁ versus polymer volume fraction) can be well described by a polynomial of third-degree in both the binary and the ternary solutions of the polymers. The solvent–segment interaction parameters exhibit a slight dependence on the polymer concentration. For each binary solution, the χ₁₂−v₂ function can be fitted by a straight line wich has a small positive slope. In the mixtures of two polymers, the values of the segment–segment (χ₂₃) interaction parameters were close to zero or sligthly negative (χ₂₃ 0 ± 0.03), indicating that under the studied conditions, the polymers in the ternary solutions are compatible.     

The formula of anchoring energy for a nematic liquid crystal

The interface energy for a nematic liquid crystal (NLC) is considered as the sum of potential energy between LC molecules and molecules of the substrate surface, and a formula for anchoring energy is derived by elementary principles. The anchoring energy for a NLC should have two terms, the first term is the same as the Rapini-Papoular expression, the second is related to the normal of interface and resultes from the biaxial property of a NLC induced by interface. Hence there are two anchoring coefficients, W₁ and W₂. We demonstrate that W₁ is equal to the tilt angle strength A_θ, and W₂ corresponds to the difference between A_θ and the azimuthal strength A_ϕ. Thus A_θ-A_ϕ is due to the biaxial property of the NLC near the interface. Applying this formula to the twisted NLC cell, we discuss the threshold and saturation field, as well as the maximal tilt angel θ_m with respect to A_θ/A_ϕ. Previously proposed formulae are discussed from our point view.     

Elastic deformations in a magnetic field of a liquid-crystalline polymer with mesogenic groups in the main and side chains

Orientational elastic deformations in a magnetic field and phase transition temperatures of a thermotropically mesogenic “combined” aromatic polyester with mesogenic groups, both in the main and in the side chains, have been investigated in the range of 900 to 10,200 mol. wt. It was shown that in this molecular weight range the birefringence of a completely oriented nematic and correspondingly, the degree of its orientational order S are independent on molecular weight. When the relative temperature ΔT changes from −2 to −30°C the orientational order parameter increases from 0.35 to 0.55. The bend elasticity constants K₃ coincide in the order of magnitude with those for high and low molecular weight nematics investigated previously and their dependence on molecular weight has not been detected.     

Effect of terminal polar substituents on the nature of smectic A liquid crystals of a series of 4-(4'-octyloxybenzoyloxy)benzylidene-4'-substituted anilines

The nature of smectic A liquid crystals and the phase transitions from smectic A to nematic phases are studied in the homologous series of 4-(4'-octyloxy-benzoyloxy)benzylidene-4'-substituted anilines, in which the substituents are H, F, Cl, Br, I, NO₂ and CN. Measurements have been performed for the dipole moment of the molecule, the smectic A lattice period, the temperatures and the entropies of phase transitions, and the temperature dependence of the orientational order parameter, all of which provide information on the intermolecular pair potentials. It is shown that the introduction of a terminal polar substituent brings about counteracting contributions to the stability of the smectic A state. It is suggested that the reentrant nematic phase transition can appear in the strongly polar mesogens if the extent of antiparallel association of the molecules increases on lowering the temperature.     

Elastic constants of uniaxial nematic liquid crystals: A comparison between theory and experiment

Using the unified molecular theory developed in our earlier paper (1992, Phys. Rev. A, 45, 974) we study in detail the influence of molecular interactions on the fundamental elastic properties of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. The expressions for the 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 the structural parameters which involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. Numerical calculations are done for a model system, the molecules of which have prolate ellipsoid of revolution symmetry and interact via a pair potential having both repulsive and attractive parts. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution. The attractive potential is represented by the dispersion and electrostatic interactions. Results for the elastic constants are reported for a range of molecular length-width ratio, temperature, density and molecular parameters and are compared with the experimental values of p-azoxyanisole (PAA) and 4'-n-octyloxy-4-cyanobiphenyl (8OCB). It is found that the inclusion of electrostatic interactions reduces the values of the ratios K₂/K₁ and K₃/K₁. The absolute values of the elastic constants and their ratios are in good agreement with the experimental and computer simulation values. The temperature dependence of the elastic constants and their ratios is studied. It is observed that the twist elastic constant has a weak temperature dependence but a pronounced influence is observed on the bend moduli. We also observed a pronounced increase in the values of the twist and bend elastic constants on approaching the nematic-smectic A transition temperature.     

NMR field-cycling study of proton and deuteron spin relaxation in the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl

NMR field-cycling measurements of the deuteron spin relaxation dispersion T₁(v) for the fully deuteriated nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB-d₁₉) over a broader Larmor frequency range (v≈10 kHz to 30 MHz) than reported so far in the literature basically confirm the magnetic relaxation mechanisms previously observed by frequency dependent proton spin studies of various nematogenic molecules, namely collective nematic modes of the director field in the kilohertz regime, and anisotropic reorientations of individual molecules (mainly self-diffusion for the protons and mainly rotations about the long axis for the deuterons) in the megahertz range. Within the experimental error limits such a model allows a self-consistent interpretation of the available deuteron and proton T₁(v) results for deuteriated or protonated 5CB, respectively. In particular, the magnitudes of the measured order fluctuation contributions are in approximate accordance, i.e. within a factor of less than two, with theoretical estimates from NMR line splittings and the relevant material parameters. More exact and more extensive deuteron studies are needed to locate the origin of the observed minor inconsistency.     

NMR relaxation of rigid molecules in the nematic phase of a discotic liquid crystal

Frequency and temperature dependent NMR relaxation measurements were performed on deuteriated benzene, pyrene and triphenylene dissolved in the nematic phase of a discotic liquid crystal. The results show a strong frequency dependence of the spectral densities. Based on the symmetries of the system and the usual model for director fluctuations this frequency dependence should be equal for J₁ and J₂. From fitting the commonly used model of rotational diffusion and director fluctuations to the data we see that this is not the case for benzene and triphenylene, even though the fits themselves are satisfactory. Values for the elastic constants, effective viscosity and translational diffusion in similar discotic liquid crystals do not account quantitatively for the frequency dependence of benzene. For both pyrene and triphenylene quantitative comparison was impossible due to lack of translational diffusion data. We also find that the so-called cut-off wave-length is of the order of the dimensions of the liquid crystal molecules, just as in ordinary nematics.     

Calculating elastic constants of bent–core molecules from Onsager-theory-based tensor model

The orientational elasticity of the uniaxial and the biaxial nematic phases is deduced earlier. For bent–core molecules with hardcore interaction, we examine how the molecular shape affects the elastic constants of these phases. The calculation is built on a tensor model based on the Onsager theory. The elastic constants are expressed by the coefficients in the tensor model, and these coefficients are derived from molecular parameters. We calculate the elastic constants of bent–core molecules as functions of the bending angle, concentration and thickness. We also examine the elastic constants of star molecules, where we focus on the effect of the extra arm.     

Dielectric and elastic properties of a nematic phase induced by charge transfer interaction in a binary system containing disc-shaped molecules

The dielectric constants and the elastic coefficients for splay (K₁) and bend (K₃) of the charge transfer induced nematic (N_c) phase of tridecyl pentakis(phenylethynyl)phenyl ether (1) doped with different amounts of 2,4,7-trinitrofluorenone (2) were determined by studying the electric field induced bend deformation using the capacitance method. A negative dielectric anisotropy was observed. For the bend elastic constant K₃ values up to 22 × 10^-12 N are found which are one order of magnitude higher than the respective values of discotic nematic (N_D) phases. Values of 0·6-0·8 are obtained for the ratio K₁/K₃; these show a minimum for the equimolar complex.