Order In Nematic Liquid Crystals Research Articles

The orientational order in nematic liquid crystals from birefringence measurements

Various methods of order parameter determination from optical measurements are compared. Measurement results of birefringence and refractive index of liquid-crystalline 4'-pentyloxy-4-cyanobiphenyl (OCB) in the nematic phase are reported. Using these data, the polarizability anisotropy was calculated for both Vuks and Neugebauer local field models. Polarizabilities calculated in this way were applied to determine /spl Delta//spl alpha/ (polarizability anisotropy in the case of perfect orientation) using either Haller's or Subramhanyam's normalization procedures. These procedures enabled the calculation of the orientation order parameter. Polarizabilities calculated using both local field models and both normalization procedures have been compared. The values of polarizability anisotropy for both local electric field models differ significantly (/spl les/30%). No criterion is known to decide which value is correct. To avoid the determination of uncertain /spl alpha//sub i/ and /spl Delta//spl alpha/ values, a simple procedure was used for evaluation of S, based solely on birefringence measurement. This procedure gave very reasonable results.

Generalized mean-field potential description for ferroelectric ordering in nematic liquid crystals.

Ferroelectric ordering in a nematic liquid crystal system is described using a generalized mean-field potential including effective potentials for both axial and polar interactions. From a self-consistent numerical analysis, a complete phase diagram is obtained as a function of the axial and polar interaction potential strengths. The obtained phase diagram exhibits not only the usual isotropic-nematic phase transition but also nematic-ferroelectric nematic and direct isotropic-ferroelectric nematic phase transitions with a tricritical point among the phases. The phase transition behaviors and the angular orientational distribution function of the molecules were investigated by studying the dependence of the polar and the axial order parameters on the reduced temperature. Moreover, the other polar order parameters responsible for second-harmonic generation (SHG) were also investigated in the generalized mean-field potential description. As a concrete example, we performed a quantitative analysis of the SHG signal reported previously in a lyotropic poly L-glutamate system, detailing the relationship between the angular distribution function and the order parameters based on our potential model. This clarifies the nature of the ferroelectric phase responsible for SHG in nematics.

Molecular order in nematic liquid crystals from shape-dependent repulsive and attractive interactions

A molecular model for orientational ordering in liquid crystal phases is presented. A van der Waals picture is adopted, with repulsive and attractive interactions described, respectively, in terms of excluded volume and surface contact interactions for pairs of molecules. The model, based on a realistic representation of the molecular structure, is applied to the nematic phase of para-azoxyanisole (PAA). Temperature and pressure dependence of order parameters is analyzed, by discussing the role played by repulsive and attractive interactions between molecules.

Magnetic-Field-Induced Weak Order in Nematic Liquid Crystals Formed by Biaxial Molecules

Nematic liquid crystal system of interacting biaxial particles via dispersion forces is studied. The molecular orienting potential form in a magnetic field is given for the first time. Weakly ordered isotropic phase is treated in the two-particle cluster approximation. Taking account of the molecular biaxiality, it is found that the ratio of the lowest supercooling temperature T* to the nematic-isotropic phase transition temperature TC approaches the observed value, and the validity of the mean field theory is clarified.

Ferroelectricity in Liquid Crystals

After summarizing ferroelectric and antiferroelectric liquid crystals (LCs) in liquid crystals so far discovered, two materials exhibiting a proper ferroelectricity are reported; (1) polar order in nematic LC of aromatic polyesters and (2) ferroelectric switching in a lyotropic liquid crystal of polypeptide. In the polypeptide LC, strong second-harmonic generation (SHG) was observed by applying an electric field, and the phase of the SH field was reversed by reversing the field, indicating the ferroelectric switching of the nonlinear polarization. SHG was also observed in the unperturbed helical state when the incident light with the wavelength the same as the helical pitch is passed through along the helical axis. In the aromatic polyester LC, SHG arises when the degree of polymerization is larger than 20. It is proposed that these polar organization originates from the dipole-dipole interaction, namely the proper ferroelectricity.

Kinetics of phase ordering of nematic liquid crystals confined in porous media.

Employing a time-dependent Ginzburg-Landau model, we investigate the influence of a random field on the phase ordering kinetics of nematic liquid crystals. We find that in the scaling regime the effect of random field (slowing down the growth of nematic) dominates over initial conditions for spatial dimensionality d< or =2, whereas for d>2 the random field has all its effect in the "initial-growth" regime. In this last case the mere confinement of liquid crystals is insufficient to produce slow growth of the nematic order.

Monte Carlo simulations of solute ordering in nematic liquid crystals: Shape anisotropy and quadrupole-quadrupole interactions as orienting mechanisms

Monte Carlo computer simulations were used to investigate the effects of shape anisotropy and electrostatic interactions as mechanisms for orientational ordering of solutes in nematic liquid crystals. The simulation results were analyzed in terms of two theories of solute ordering which derive mean-field orientational potentials from the intermolecular pair potential. In the calculations, solute and solvent molecular shapes were approximated by hard ellipsoids. Most simulations also incorporated the interaction between point quadrupole moments placed at the centers of the ellipsoids. In the hard-core systems, orientational order parameters and distribution functions were calculated for a collection of different solutes under a variety of conditions. A theory due to Terzis and Photinos [Mol. Phys. 83, 847 (1994)] was found to underestimate the effect of shape anisotropy on orientational ordering drastically. The introduction of an effective solvent packing fraction was unable to improve the predictive power of the theory significantly. The quadrupolar systems were used to investigate a mean-field model for solute ordering which considers an interaction between the solute molecular quadrupole moment with an average electric-field gradient. The simulations indicate that the electric-field gradient sampled by the solute is highly dependent on the properties of the solute, contrary to some experimental evidence. Further, the effects of the intermolecular quadrupolar interactions on orientational ordering and the electric-field gradient were analyzed using a mean-field potential derived here and based on the theory due to Emsley, Palke, and Shilstone [Liq. Cryst. 9, 649 (1991)]. This model was found to provide a qualitatively correct but quantitatively imprecise prediction of orientational ordering.

1-D models for thin filaments of liquid-crystalline polymers: Coupling of orientation and flow in the stability of simple solutions

Slender asymptotic fiber models are derived from Doi-type 3-D equations for free surface flows of liquid-crystalline polymers. Leading order equations and self-consistent corrections are presented for a variety of physical regimes. We then explore the coupling of orientation effects to slender elongational flow behavior, with particular focus on the interplay between the Rayleigh capillary instability and both stabilizing and destabilizing orientation behavior. In the simple context of constant solutions, we identify physical regimes and precise conditions under which the Rayleigh instability may be completely arrested, as well as other regimes where orientation reduces but does not cancel capillary instability. In addition, we identify sources of additional orientation-dominated instabilities that are evident in both the uniaxial and biaxial nematic liquid crystal order parameters. These models and stability analyses lay the foundation for applications to fiber spinning processes.

Kinetics of phase ordering of nematic liquid crystals in a confined geometry

Employing a time-dependent Ginzburg-Landau model, we investigate the phase ordering kinetics of nematic liquid crystals confined in a narrow pore. We consider various orientations of the surface field and compute domain growth laws and scaling functions. In the absence of any anchoring field we find that (and in contrast to a confined binary liquid mixture) mere confinement of the liquid crystals is insufficient to produce slow growth of the nematic domains owing to the vector nature of the order parameter. In the presence of a strong homogeneous anchoring, the system quickly reaches a nematic state. On the other hand, for homeotropic anchoring, the liquid crystal takes on an XY character and the growth law exponent crosses over from 1/2 to 1/4 as the field strength is increased. \textcopyright{} 1996 The American Physical Society.

Investigation of the interfacial order of nematic liquid crystal on photopolymer coated conducting glass substrates with a scanning tunneling microscope

High resolution images of individual molecules of the liquid crystalline material adsorbed on a photopolymer treated transparent conducting (indium oxide coated) glass plate have been obtained with a scanning tunneling microscope (STM). The ultrathin layer of the photopolymer poly-vinyl-4-methoxy-cinnamate (PVMC) on the conducting glass plate was deposited by the bulk induced alignment technique reported earlier [S. C. Jain and H.-S. Kitzerow, Appl. Phys. Lett. 64, 2946 (1994)]. The liquid crystal molecules exhibit a positional order, in addition to a high degree of orientational order of the bulk nematic. This surface ordering of the nematic liquid crystal at the polymer interface is quite different from the ordering observed on graphite and molybdenum disulphide substrates. A small ensemble of molecules show antiparallel ordering of the cyano-phenyl-cyclo-hexane molecules in agreement with the calculations of Schadt et al. [Liq. Cryst. 5, 293 (1989)].

Theory of phase-ordering kinetics

The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time-dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, e.g. vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings, monopoles) provides a unifying framework for discussing coarsening in these different systems.

Structure factor for phase ordering in nematic liquid crystals.

We present an approximate analytical calculation of the time-dependent structure factor for the phase-ordering dynamics of nematic liquid crystals. The structure factor is found to exhibit a ${\mathit{k}}^{\mathrm{\ensuremath{-}}5}$ tail, due to the presence of 1/2 integrally charged string defects. Our theoretical results are in good agreement with simulation data, and are consistent with recent experiments.

Cell dynamics simulation for the phase ordering of nematic liquid crystals.

A discrete model is presented to describe the dynamics of nematic liquid crystals for the case where topological defects dominate the spatial pattern. A numerical study is given of the annihilation kinetics of the defects in the two-dimensional nematic system with ${\mathit{P}}^{2}$ symmetry. The structure factor is found to obey a scaling law S(k,t)=〈k${\mathrm{〉}}_{\mathit{t}}^{2}$g(k/〈k${\mathrm{〉}}_{\mathit{t}}$) where the first moment 〈k${\mathrm{〉}}_{\mathit{t}}$ varies as 〈k${\mathrm{〉}}_{\mathit{t}}$\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}0.42}$. The asymptotic power-law tail g(x)\ensuremath{\sim}${\mathit{x}}^{\mathrm{\ensuremath{-}}4.5}$ is found.

Theory of phase ordering kinetics

The theory of phase-ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench.How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor ®elds. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these diA erent systems.

Phase-ordering dynamics of nematic liquid crystals.

We study phase ordering in nematic liquid crystals using cell-dynamics simulations for d=2, n=2, and d=3, n=3. The tail in the structure function decays as ${\mathit{k}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\chi}}}$, with \ensuremath{\chi}=4.0\ifmmode\pm\else\textpm\fi{}0.1 for d=2 and \ensuremath{\chi}=5.3\ifmmode\pm\else\textpm\fi{}0.1 for d=3. We compare these values to results of Bray and Puri [Phys. Rev. Lett. 99, 99 (1992)] for a vector order parameter and to experimental measurements. For the d=3 system the characteristic length scale in the system varies as L(t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\varphi}}}$, with \ensuremath{\varphi}=0.44\ifmmode\pm\else\textpm\fi{}0.01.

Influence of K 24 on the structure of nematic liquid crystal droplets

Abstract A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K 24, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K 24 term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.

Computer simulation studies of the dependence on density of the orientational order in nematic liquid crystals

Abstract Simulations of the temperature dependence of the nematic orientational order parameter, [Pbar] 2, at different densities have been made using the Gay-Berne potential. The results are used to calculate Γ = −(∂In T/∂ IN V) [Pbar] 2, which is a measure of the relative sensitivity of [Pbar] 2 to temperature and density. Previous experimental measurements of Γ have obtained values in the range 2–6 for real nematogens, whilst the present simulations yield Γ = 8 ± 1. Changing the Gay-Berne potential by increasing the steepness of the repulsive term increases the calculated value of Γ, whilst changing the relative well depths for side-by-side compared to end-to-end arrangements of Gay-Berne particles leaves Γ virtually unchanged. These exploratory calculations suggest that Γ is a useful parameter for testing the parametrizations of model potentials.

Molecular flexibility and orientational ordering of nematic liquid crystals

The ‘‘chord model’’ of flexible alkane solute ordering in the nematic phase [D. J. Photinos, E. T. Samulski, and H. Toriumi, J. Phys. Chem. 94, 4688 (1990); 94, 4694 (1990)] is extended to prolate mesogen molecules with a single alkyl tail, and the physical properties of two homologous series, 4,4′-n-alkylcyanobiphenyls and 4,4′-n-alkyloxycyanobiphenyls, in neat nematic phases are evaluated. The chord model of the mesogen’s anisotropic interactions yields a consistent description of the essential features of the chain order profile (derived from deuterium nuclear magnetic resonance) and the even–odd variation of thermodynamic quantities associated with the nematic–isotropic transition. Very accurate agreement with experimental observations is obtained using the standard rotational isomeric state description of the tail–chain’s flexibility along with a minimal form of the self-consistent anisotropic potential (i.e., only two coupling constants determine the strength of orientation dependent interactions, one for the biphenyl core and one for the aliphatic chord segments). There is remarkable compatibility among the values of optimized coupling constants obtained from modeling the chain segmental order parameters and the mesophase transition temperatures. Moreover, these coupling constants evaluated for aliphatic chord segments in the neat mesogens show quantitative agreement with the values obtained for simple alkane solutes in nematic solvents. These findings suggest that the chord model, which explicitly represents molecular shape anisotropy (excluded volume effects) in conjunction with molecular flexibility, provides a very good description of complex molecules in liquid crystals.

New optical methods to study director orientation in liquid crystals

We report new optical methods useful to investigate the orientational order of nematic liquid crystals. The first one uses a linear optical technique and a variable-thickness cell to get a precise measurement of the anchoring energies at the boundaries. The second one exploits the nonlinear self-phase modulation to evaluate the elastic anisotropy of a nematic liquid crystal. Examples are reported of measurements performed on hybrid aligned liquid crystals.

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.