Landau theory of the nematic-isotropic phase transition

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 discharge modes of a thermionic low pressure discharge (p<1Pa) are investigated with the one‐dimensional particle‐in‐cell simulation codes PDP1 and XPDP1 [C. K. Birdsall, IEEE Trans. Plasma Sci. 19, 65 (1991)]. The simulation results provide a model approach for stable discharge modes, hysteresis, and for nonlinear relaxation‐oscillations. During this potential‐relaxation instability, nonlinear structures, e.g. electron holes and double layers, are observed. A Pierce–Buneman‐mode is suggested as a trigger mechanism for the onset of the instability. The detailed oscillation process can be subdivided into three distinct phases: expansion phase, double layer phase, and relaxation phase. This allows one to explain the parameter dependencies of the oscillation frequency. For a periodically driven discharge, mode‐locking in a period‐2 state is found and explained by the model. The mode‐locking phenomenon is studied systematically. The results of the simulations are well confirmed by experimental observations presented in Part II of this paper [T. Klinger et al., Phys. Plasmas 2, 1822 (1995)].

Nonlinear dynamical behavior of thermionic low pressure discharges. I. Simulation

Magnetic field induced order in uniaxial nematics: A comparison of Landau-de Gennes and Maier-Saupe theories

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

We study the effects of an external field on the isotropic-nematic transition in liquid-crystalline substances. The theoretical technique employed is called the "orientationally averaged pair correlations" approximation. It takes into detailed account spatial correlations between the molecules while treating orientational order in a mean-field-like manner. The results obtained for MBBA ($4\ensuremath{-}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{e}\ensuremath{-}4\ensuremath{'}\ensuremath{-}n\ensuremath{-}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}$) are compared to those of the Maier-Saupe theory and the Landau-de Gennes theory. We determine the paranematic-nematic coexistence curve, the temperature-external field phase diagram, the Cotton-Mouton coefficient, the maximum supercooling temperature, critical exponents, and the relation between the transition temperature and the electric field in laser-induced isotropic-nematic transitions. These results are compared to experimental data. Their implications are discussed.

Isotropic-nematic transition in an external field

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.

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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.

Chia-Wei Woo

Papers

Isotropic-nematic transition in an external field

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

Spatial Correlations in Nematic Liquid Crystals