Perturbation theory for nematic liquid crystals of axially symmetric molecules: Numerical results at high pressures including second- and fourth rank orientational order parameters

A statistical mechanical perturbation theory is applied to study the thermo-dynamic properties of nematic liquid crystals at the nematic-isotropic (N-I) phase transition under pressure, retaining second- and fourth-rank long-range orientational order parameters. We report calculations for a hard ellipsoidal system superposed with an attractive interaction and subjected to different external pressures. The repulsive interaction is represented by a repulsion between hard ellipsoids characterized by a length-to-width ratio and the interaction arising from the dispersion interaction between two asymmetric molecules represents the attractive interaction. The inclusion of the fourth-rank order parameter in the effective one-body potential ψ(Ω) does not lead to a significant overall improvement. The influence of pressure on the stability, ordering and thermodynamic functions at the N-I transition is analysed. We find that our theoretical predictions are in accordance with experimental observations.     

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.     

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.     

Calculation of long-range orientational order parameters in impure nematic liquid crystals using an extended van der Waals model

For the atended van der Waals model of a binary nematic system consisting of rigid biaxial molecules, we consider the following properties: the relation between the orientational order parameters of a nematic liquid crystal (NLC) S⁽¹⁾ and a nonmesomckphic impurity S⁽²⁾, the relation between S⁽²⁾ and the biaxiality parameter D⁽²⁾ of the impurity, and the lowered clearing temperature of NLC upon dissolution of the nonmesogen. The dependence of these characteristics on the fom and size of component molecules and the intermolecular attraction potential is analyzed. The model reproduces the experimental dependence of S⁽²⁾ and D⁽²⁾ on temperature and structure of the nematic matrix.Scientific Research Institute of Chemistry, St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 106–115, September–October, 1993.Translated by L. Smolina     

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.     

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

Abstract

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-d ₁₁) and 4-n-pentyl-4′-cyanobiphenyl (5CB-d ₁₉). The systems studied were low concentrations of 1CB-d ₁₁ and 5CB-d ₁₉ 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.     

On the determination of order parameters for homogeneous and twisted nematic liquid crystals from Raman spectroscopy

Traditional approaches to the use of Raman spectroscopy as an aid to the determination of local order parameters in liquid crystalline materials have employed polarizations of the excitation source and/or the analyser which are orthogonal to the liquid crystalline director. The present paper describes a Raman study, which seeks to take advantage of the additional information available from examining the complete range of orientations of the director in relation to these polarization directions. A theory is developed which shows how it is possible to use this additional information to derive more reliable values of the P₂ and P₄ local order parameters in homogeneous and twisted nematic liquid crystal cells.     

A specialized apparatus for the study of liquid crystals at high pressures

Abstract

A pressure system specially designed for the study of liquid crystal materials at high pressures up to 4kbar is presented. The pressure system is based on a hydrostatic screw injector and uses either oil or gas as the pressure transmitting medium. The type of measurements which can be performed with the instrument include polarized microscopy, optical spectroscopy, electrooptic and electrical measurements. The different measurements performed place specific constraints on the design of the apparatus and the pressure cells, and details are given. A preliminary study of the smectic A modification of the twist grain boundary phase (TGB_A) at high pressures is presented. The pressure versus temperature phase diagram shows (i) a negative gradient of the TGB_A/isotropic phase boundary line and (ii) that the TGB_A phase does not exist at pressures above about 250 bar. Following Lubensky's analogy between the TGB_A phase and type II superconductors, the disappearance of the TGB_A phase at high pressure may imply that the Landau-Ginsburg parameter K decreases with pressure.     

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.     

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.     

Analytical solutions for rotational diffusion in the mean field potential: application to the theory of dielectric relaxation in nematic liquid crystals

A theory of dielectric relaxation in nematics is developed for a molecular dipole moment directed at an arbitrary angle to the molecular long axis. Both exact and simple approximate analytical formulae for the longitudinal and transverse components of the complex dielectric permittivity tensor are obtained for the non-inertial rotational Brownian motion of a molecule in the mean field potential of Maier and Saupe. It appears that both longitudinal and transverse relaxation processes are effectively described by two Debye type mechanisms with corresponding relaxation times and dielectric strengths expressed in terms of the order parameter. The generalization of the theory for an arbitrary axially symmetric mean field potential is given.     

Orientational order of difluorinated liquid crystals: a comparative 13C-NMR, Optical, and dielectric study in nematic and smectic B phases

Structural and orientational order properties of 3Cy2CyBF2 and of 5CyCy2BF2 have been investigated by means of (13)C-NMR, optical, and dielectric spectroscopy methods. In the case of NMR, order parameters have been independently obtained from the analysis of either (13)C-(19)F dipolar couplings or (13)C chemical shift anisotropies, both measured from (13)C-{(1)H} NMR static spectra. The assignment of the (13)C resonances has been carried out thanks to the comparison with solution state spectra and DFT calculations, and the relevant geometrical parameters and (13)C chemical shift tensors needed to derive orientational order parameters have been calculated by DFT methods. In the analysis of (13)C-(19)F dipolar couplings, empirical corrections for vibrations and anisotropic scalar couplings have been included. Dielectric measurements have been performed over a broad frequency range for two orientations of the nematic director with respect to the measuring field. At low frequencies (static case) a positive dielectric anisotropy has been determined, which has enabled the calculation of the order parameters according to a well-tested procedure. At high frequencies the dielectric anisotropy changes its sign, a property which can be useful in designing a dual addressing display. The nematic order parameter determined from optical, dielectric, and NMR methods have been compared: their trends with temperature are very similar, apart from some slight shifts, and were analyzed by Haller and Chirtoc models. The differences among the results obtained by the four methods have been discussed in detail, also with reference to the assumptions and approximations used in each case, and to the results recently reported for similar fluorinated nematogens. The presence of a non-negligible order biaxiality has been related to the presence of a CH2CH2 bridging group, linking one cyclohexylic unit with either the other cyclohexyl or the phenyl ring.     

2H NMR spectroscopy of liquid crystals: structure and orientational order of a chiral smectogen in its A, C* and J* phases

²H NMR spectroscopy is employed to investigate the orientational order, molecular structure and phase transitions of the chiral smectic liquid crystal 1-methylheptyl 4'-(4-n-decyloxybenzoyloxy)biphenyl-4-carboxylate (10B1M7), showing smectic A, C* and J phases, as well as several sub-smectic C* phases. Two optically pure, differently deuteriated isotopomers have been purposely synthesized and studied.     

2H NMR spectroscopy of liquid crystals: structure and orientational order of a chiral smectogen in its A,C* and J* phases

²H NMR spectroscopy is employed to investigate the orientational order, molecular structure and phase transitions of the chiral smectic liquid crystal 1-methylheptyl 4'-(4-n-decyloxybenzoyloxy)biphenyl-4-carboxylate (10B1M7), showing smectic A, C* and J phases, as well as several sub-smectic C* phases. Two optically pure, differently deuteriated isotopomers have been purposely synthesized and studied.     

Simulations of lipid crystals: Characterization of potential energy functions and parameters for lecithin molecules

We evaluate an empirical potential energy function and associated parameters for classical molecular dynamics simulations of lecithins, a common class of lipid. The physical accuracy of the force field was tested through its application to molecular dynamics simulations of the known crystal structures of lipid molecules. Average atomic positions and molecular conformation are well maintained during the simulations despite considerable thermal motion. Calculated isotropic temperature factors correlate highly with those from experiment.     

New symmetric azobenzene molecules of varied central cores: Synthesis and characterisation for liquid crystalline properties

A new series of azobenezene liquid crystals (LCs) was designed and synthesised by known and straightforward methods. The central connecting cores of the molecules varied viz., benzene/naphthalene/biphenyl. The molecular structures were confirmed by infrared, UV, nuclear magnetic resonance spectroscopic techniques. The LC texture and thermal phase behaviours were investigated by polarising optical microscopy and differential scanning calorimetry. Smectic B phase was found in biphenyl-derived azobenzene ester. The effect of central core on LC properties was investigated. The decreased angle at central connecting core suppressed the melting points, phase transition temperatures without losing LC properties, whereas, in moderate angle compounds LC properties were suppressed. The compounds with increased angle at central core favours rich mesomorphism.     

Calculation of Verdet constants with time-dependent density functional theory: implementation and results for small molecules

We report the implementation of a method by which to calculate Verdet constants for molecules. The method is based on gauge-including atomic orbitals (GIAOs) and density functional theory. Calculations based on this method afford magneto-optical rotations of the right magnitude for the molecules H2, N2, CO, HF, CH4, C2H2, H2O, and CS2. The results are in satisfactory agreement with experiment. We investigate the dependency of the results on the gauge origin if GIAOs are not chosen, the convergence of the results with the size of the basis set for AOs and GIAOs, and for H2O and CS2 a comparison of gas-phase and liquid phase values. For the small molecules studied here, large polarized basis sets with diffuse functions are required to obtain well converged results. The use of an asymptotically correct Kohn-Sham potential is advantageous.