Theory Of Nematic Liquid Crystals Research Articles

Polar Anchoring Effect on Bistable Nematic Liquid Crystal Display

The switching process of BiNem liquid crystal displays (LCDs), which has been so far argued, is reexamined from the viewpoints of anchoring breaking and flow effects. By numerical simulation based on the continuum theory of nematic liquid crystals, the switching process between two stable states was investigated by changing the surface anchoring condition of BiNem LCDs to optimize bistable conditions. From the numerical results of the director and the flow distributions, polar anchoring breaking was distinguished clearly from azimuthal anchoring breaking in bistable switching. The bistable switching regime was observed to be limited by the polar anchoring strength at the slave plate; therefore, the polar anchoring strength at the slave plate was optimized for bistable switching. Furthermore, a BiNem cell was fabricated based on the numerical results, and bistable switching was confirmed.

Continuum theory for nematic liquid crystals with tensorial order

From a variational principle, we derive the equations of motion for nematic liquid crystals described by a second-rank order tensor. The only constitutive ingredients are the densities of the free energy and the dissipation, both subject to appropriate invariance requirements. We show that this theory is sufficiently general to encompass others as special cases. Comparing this theory with other theories also suggests criteria to avoid the proliferation of viscosity coefficients.

Frank Matthews Leslie. 8 March 1935 – 15 June 2000

Frank Leslie was a distinguished applied mathematician, who was above all foremost in creating the modern continuum theory of nematic liquid crystals in the late 1960s. This theory is now known as the Ericksen-Leslie theory, and the crucial elements in it as Leslie coefficients. After developing the hydrodynamic theory of nematic liquid crystals, he went on to perform a similar task in the 1990s for smectic liquid crystals. He also actively collaborated with experimentalists and engineers involved in liquid crystal applications, and his work has been extremely influential in the development of liquid crystal display (LCD) device technology.

A Molecular Field Theory for Uniaxial Nematic Liquid Crystals Formed by Non-Cylindrically Symmetric Molecules

Most molecular theories of nematic liquid crystals assume that the constituent molecules are cylindrically symmetric. However, although this may be a useful approximation the molecules of real nematogens are of lower symmetry; here we develop a theory for an ensembles of such particles based on a general expansion of the pairwise intermolecular potential together with the molecular field approximation. The dependence of the orientational properties of the uniaxial mesophase on the deviation from molecular cylindrical symmetry is calculated from the series expansion of the pseudo-potential. In these calculation the number of arbitrary parameters in the orientational pseudo-potential is reduced by assuming that the anisotropic intermolecular potential originates solely from dispersion forces. The theoretical predictions for the values of the ordering matrix and the entropy change at the nematic-isotropic, transition are found to be in good agreement with those observed for 4,4'-dimethoxyazoxybenzene. In addition, the theory provides a reasonable account of the temperature dependence of the order parameter at constant volume for this nematogen. The allowance for deviations from molecular cylindrical symmetry appears to remove many of the discrepancies between the Maier-Saupe theory and experiment

Magnetization dynamics, rheology, and an effective description of ferromagnetic units in dilute suspension.

The rheological properties of a dilute suspension of ellipsoidal ferromagnetic particles in the presence of a magnetic field are studied on the basis of a kinetic model, where the flow and magnetic external fields couple in qualitatively different ways to the orientational behavior of the suspension. In the uniaxial phase the stress tensor is found to be of the same form as in the Ericksen-Leslie theory for nematic liquid crystals in the steady state. Expressions for a complete set of viscosity coefficients in terms of orientational order parameters are worked out. In the low Péclet number regime, the viscosity coefficients are given as explicit functions of the magnetic field and a particle shape factor, where the shape factor may equally represent a nonspherical unit (agglomerate, chain) composed of spherical particles. Effects due to possible flow-induced breakup of units are not covered in this work. Further, by considering the magnetization as the only relevant variable, a magnetization equation within an effective field approach is derived from the kinetic equation and compared to existing magnetization equations. The alignment angle of the magnetization and the first and second normal stress coefficient are studied for the special case of plane Couette flow. The assumptions employed are tested against a Brownian dynamics simulation of the full kinetic model, and a few comparisons with experimental data are made.

The evolution equation for a disclination in a nematic liquid crystal

We extend the EricksenLeslie theory for nematic liquid crystals to account for the presence of disclinations. To achieve this, we use Gurtin's theory of configurational forces and obtain an evoluti...

FRANK ELASTICITY REVISITED: CONTRIBUTION OF ROTATIONAL ENTROPY

In previous molecular theories of nematic liquid crystals, rotational entropy, or the entropy loss due to molecular alignment, has been believed to make no contribution to Frank elasticity. We show that this is not true, using a field-theoretical method developed in polymer physics. We also give an exact expression of the contribution of rotational entropy to Frank elasticity for rod-like liquid crystals in terms of the orientational tensor order parameter.

Liquid crystals of polyelectrolyte networks.

The Onsager theory of nematic liquid crystals is extended to rigid polyelectrolytes cross-linked by polyvalent ions. Recent synchrotron x-ray diffraction experiments showed that dilute, birefringent networks are formed under these conditions. The application of Onsager theory to this system leads to the prediction of the existence of a range of exotic mesophases such as the "cubatic," the "tetratic," and the "trigatic." The exotic network phases appear on the border of regions of phase coexistence of network phase with isotropic material (at low polyvalent ion concentration) and with dense bundles (at high polyvalent ion concentration).

Reactivity of liquid crystals in the region of nematic — isotropic phase transition.

Abstract In the present paper a statistical-thermodynamic theory of nematic liquid crystals, developed by us on the basis of the fundamentals of statistical physics and chemical thermodynamics with the help of experimental data for the activation energy of the viscous flow of nematic and isotropic liquids is suggested. Using the theory and as an illustration a number of nematics from mesogenic molecules with chemically inactive groups in the terminal position, physical-chemical characteristics are obtained, which help to better revealing the mechanism of the viscous flow of liquid crystals in nematic and isotropic phases, their reactivity in such processes as a displacement of nematic-isotropic equilibrium taking place at phase transition, conformational changes of molecules establishing the composition of equilibrium subsystems and the time of their relaxation.

Surface Order Parameter and Polar Anchoring Energy in Nematic Liquid Crystals

The trends of temperature dependence of the surface order parameter and of the anchoring strength coefficient are theoretically evaluated in the Landau-de Gennes phenomenological theory for nematic liquid crystals. The cases of planar, homeotropic and tilted alignment at a planar limiting surface are considered. It is shown that the cases with surface order parameter greater than the bulk one or smaller than this can occur in function of the phenomenological coefficients in the surface free energy expression. The anchoring strength coefficient, W, diminishes when temperature approaches the nematic-isotropic point, after passing through a maximum in most of cases. The possibility of a non-zero anchoring strength at temperatures above the transition temperature is revealed. The obtained trends of W(T) describe well a large variety of experimental results from literature.

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.

Non-local description of nematic liquid crystals

A non-local description of nematic liquid crystals is presented. By considering a generic two body interaction, the total energy of a nematic sample is formally evaluated. It is given by a generalized non-local functional. The minimization of the total energy shows that the actual nematic tilt angle profile, characterizing the nematic director, is a solution of an integral equation that in the simplest case is of the Freedholm type. This new equation takes the place of the well known Euler-Lagrange equation used in the elastic theory of nematic liquid crystals. The existence of sub-surface deformations localized close to the limiting surfaces is studied by means of this integral equation. The analysis has been performed for cases of strong and weak anchoring, with and without external fields. The sources of the subsurface deformations are discussed in the framework of the usual Frank elastic theory.

Azimuthal anchoring of liquid crystals on surfaces with high symmetry

Substrates with a high in-plane symmetry (threefold or higher) induce multistable anchorings in nematic liquid crystals: The preferred nematic axis in the bulk can take several equivalent orientations with different in-plane directions. To elucidate the mechanisms leading to this degeneracy, we have investigated the relation between the orientational order of cyanobiphenyl molecules at the surface of phlogopite mica plates (exhibiting a threefold symmetry) and the observed bulk orientations induced by these surfaces. In particular, in-plane bulk reorientations were observed when the system was put in the presence of water vapor. These appear to be driven by changes in the tilt distribution of the surface molecules. To account for our observations, we propose an anchoring mechanism based on the coupling of the uniaxial bulk nematic order to the surface-induced threefold order present in the first molecular layer. For this purpose the Landau\char21{}de Gennes theory of nematic liquid crystals is extended to take such a coupling into account. The calculations show that the observed in-plane bulk reorientations can be induced by changes in the surface value of the scalar nematic order parameter.

Viscosities of Nematic and Discotic Nematic Liquid Crystals According to the Affine Transformation Model

An affine transformation model is used to calculate the macroscopic stress tensor for uniaxial liquid crystals. In the special case of constant degrees of alignment, it is shown to be of the form occurring in the Ericksen-Leslie director theory for nematic liquid crystals, resolving an apparent discrepancy on the form of the stress tensor. The corresponding Leslie and Miesowicz viscosities are calculated in terms of the alignment order parameters and those of the affine model. These results improve the approximate calculations of Ehrentraut and Hess [Phys. Reo. E 51, 2203 (1995)] based on a hindered rotation assumption. It is further shown that the calculated orientation-dependence of the viscosities based on the affine model is the same as that resulting from calculations based on an alternative Fokker-Planck equation for the one particle orientational distribution function.

Two Particle Cluster Theory for Nematic Liquid Crystals Confined by Parallel Planes

We present a two-particle cluster variation theory to treat the inhomogeneous nematic system confined by two parallel planes which align the surface molecules perpendicular to them. Numerical calculations are made for a film composed of 20 molecular layers. The nematic-isotropic transition temperatures for typical values of the strength of the surface field are given and the layer dependences of the order parameter are shown. The Monte Carlo simulation data are needed to demonstrate our results.

Statistical Theory of Nematic Liquid Crystals Composed of Biaxial Ellipsoidal Particles

Statistical theory of nematic liquid crystal whose constituent molecules are biaxial ellipsoids is proposed. The method is suggested which enables one to calculate exactly the second virial coefficient for the system of biaxial ellipsoidal particles and to obtain a simple approximation formula for the third one. By means of the so-called y-expansion, the thermodynamic potential of the system is constructed and equations of the thermodynamic and orientational state are obtained. The influence of the anisometric degree (i.e. the measure of biaxiality) of the particles on the features of orientational behavior and phase transitions among the isotropic, uniaxial and biaxial nematic phases is studied. A phase diagram for a system of biaxial ellipsoids has been calculated. It is shown that the so-called self-dual point takes place with high degree of accuracy. In the limiting cases (molecules are spheres or ellipsoids of revolution) our results are identical with earlier known ones.

Flow Alignment in Biaxial and Discotic Nematics

Continuum theory for nematic liquid crystals predicts two distinct types of flow alignment, one that observed in thermotropic rod-like nematics, and the second not so far observed but thought to be relevant to discotic nematics. This paper examines this latter possibility by considering recent flow alignment predictions for biaxial nematics, particularly for such materials where the molecular structure is close to discotic, and obtains results that support this claim. In addition it shows that in the disc-like limit biaxial theory reduces to that for a uniaxial nematic with viscosities consistent with this conjecture.

Periodicity in nematic liquid crystal walls.

The elastic continuum theory of nematic liquid crystals is used to show that the periodicity of the walls that are observed above the critical Frederick's field in nematic liquid crystals is closely related to the dimensionality of these structures, and that the $\ensuremath{\pi}$ symmetry of the director and the fluid flow mechanism, usually regarded as responsible for these walls, are not enough to fully explain the observed periodicity.

Optical Characterization of Homogeneous Nematic Liquid Crystal Cells Based on the Liquid Crystal Continuum Model

We formulated and applied a new algorithm based on the continuum theory of nematic liquid crystals to the characterization of the electrooptic response of homogeneous nematic liquid crystal cells. Appropriate selection of the device parameters ensures predictions of the electrooptic response which are in agreement with results of optical measurements to a precision of better than 1°. The effect of induced molecular twist and the limitations of decoupling between orthogonal polarizations are discussed.

Enhancement of optical nonlinearity in a guest-host system by nematic ordering

Second-harmonic generation (SHG) has been studied for understanding the enhancement mechanism for the second-order optical nonlinearity by the nematic (or axial) ordering in a liquid crystal doped with one-dimensional nonlinear optical (NLO) organic molecules. An extended version of the Maier-Saupe mean-field theory for nematic liquid crystals was developed to obtain analytical expressions for the second-order NLO coefficients in terms of the axial order, the polar order and the effective nematic potential. From the SHG data in a guest-host system composed ofN,N'-dimethylaminonitrostilbene molecules (0.5% by weight) and a liquid crystal, the enhancement of the second-order NLO coefficient,d33, by nematic ordering becomes almost 3, which agrees well with our theoretical predictions.