A density-functional description of liquid crystals is developed. Formally exact expansions for thermodynamic functions in terms of a direct-correlation function are given. Approximations to the direct-correlation function lead to different versions of the molecular-field theories of liquid crystals. The properties of the uniform nematic phase including the isotropic-nematic phase transition at constant pressure are discussed. Expressions are given for the change in density and order parameters at the transition in terms of the direct-correlation function of the isotropic phase. Methods for calculating the direct-correlation functions of the isotropic phase are also discussed. A formal theory for the statistical mechanics of a nonuniform liquid crystal is developed and used to derive expressions for the Frank elastic constants. This approach provides a starting point for the investigation of the phase transitions in the liquid crystals and the properties of inhomogeneous systems. A microscopic description of the Landau-de Gennes theory is also given.

Molecular theory of liquid crystals: Application to the nematic phase

The measurements of the polarized fluorescence intensity for a stilbene guest molecule dissolved in nematic liquid crystals (5CB, 7CB and PCH7) have been used to study the molecular orientational order in thin aligned samples. The temperature dependence of the order parameters ⟨P2⟩ and ⟨P4⟩ have been investigated. The attempt for the explanation of the different behaviour of ⟨P4⟩ parameter in the various liquid crystals has been undertaken. On the basis of the experimental ⟨P2⟩ and ⟨P4⟩ values some information about the orientational distribution of molecules in guest-host mixture have been obtained.

Polarized Fluorescence Studies of Orientational Order in Some Nematic Liquid Crystals Doped with Stilbene Dye

A new mechanism is proposed for the collective light-induced rotation of orientationally ordered molecules of absorbing nematic liquid crystals. The mechanism derives from the noncentral character of the light-induced change in the interaction potential of the excited and unexcited molecules and also from the anisotropy of their correlation function. Rotation is produced by the difference of the torques exerted by the intermolecular forces orienting the ensembles of excited and unexcited molecules.

On the mechanism of light-induced orientation of molecules in absorbing nematic liquid crystals

The development of sensors that are smaller, lighter weight and require less bandwidth is critical for the success of space-based and airborne imaging systems. One solution to this problem is foveated imaging, wherein a liquid crystal spatial light modulator is used to selectively enhance resolution in a wide field-of-view imaging system. Selective enhancement decreases the bulk and complexity of the optical train, while simultaneously reducing data transmission and processing requirements. This enhancement is done modulo 2/spl pi/, as such it is inherently a monochromatic correction. In this paper, we propose to overcome that limitation by introducing a switchable polarization interference filter, obtaining near diffraction limited performance over the instantaneous field-of-view (IFOV) at the wavelength(s) of interest.

Multi-spectral foveated imaging system

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Role of surface-like elastic constants in the phenomenology of confined nematics

Starting with a model intermolecular potential that includes $\stackrel{^}{\ensuremath{\Omega}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{r}$ terms to account for anisotropic steric interactions, we carry out a statistical mechanical calculation in the cell approximation, and apply it specifically to the isotropic-nematic transition of methoxybenzylidene butylaniline (MBBA). The potential is determined to fit the experimental transition temperature ${T}_{\mathrm{IN}}$ and the discontinuity in the orientational order parameter $〈{P}_{2}〉$ at transition. $〈{P}_{2}〉$ and $〈{P}_{4}〉$ are then calculated from solving a set of coupled self-consistency equations for the orientational and spatial parts of the distribution function, as are other phase-transition properties. There are improvements over model calculations which do not account for anisotropic steric effects, but the improvements are generally less than significant. The most striking result is that a stable nematic phase requires $〈{P}_{4}〉$ to be negative at and near the transition. It is a theoretical result qualitatively consistent with experimental data but has not been attained until now.

/pdf/anisotropic-steric-effects-and-negative-p-4-in-nematic-2ki7lfvulg.pdf

Anisotropic steric effects and negative 〈 P 4 〉 in nematic liquid crystals

Liquid crystals are liquids. At such densities, spatial correlations between molecules are expected to play an important role in the determination of their collective and phase transition properties. At short range, these correlations are quite anisotropic as a result of anisotropic intermolecular repulsions. We recall a molecular potential model that takes into account anisotropic forces. We show how spatial correlations are accounted for in the “orientationally averaged pair correlations” approximation (OAPC) to affect the macroscopic properties of nematic liquid crystals. We then perform a cell model calculation in which both the molecular orientational distribution and the spatial distribution about lattice sites are determined self-consistently, by solving coupled Euler-Lagrange equations which minimize the free energy. Numerical work is carried out for a simple potential without anisotropicters. We are able to determine the potential parameters which reproduce earlier OAPC results. Such an exercise illustrates how the cell approximation works and provides us with a theoretical framework for introducing anisotropic forces and pair correlations into later work. It is hoped that the latter would help remove some of the serious discrepancies between molecular theories and esperiment.

Kean Feng

Papers

Anisotropic steric effects and negative 〈 P 4 〉 in nematic liquid crystals

Spatial Correlations in Nematic Liquid Crystals