Clausius-Mossotti Function for Restricted One-dimensional Operators

Deviations from constancy of the C_M function, are considered on the basis of a one-dimensional oscillator model in which the valence electrons are assumed restricted by infinite potentials, but interact with all others through dipolar forces. A computer calculation shows that the density-dependence of C_M is qualitatively in agreement with experiment, but the temperature-dependence is negligible. An interesting feature is the occurrence of negative polarizabilities for the excited states at modest densities -indicating an insulator-to-metal transition. This result is in conflict with the basic precepts of the model which does not permit fully delocalized electronic states. However, this analysis suggests a more promising three-dimensional model which admits of realistic atomic potentials, dynamical dipolar interaction and repulsive potentials which ensure the existence of the ionized state of the atom

Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order

Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted with respect to the smectic layer normal. As in the previous papers of the series (Phys. Rev. A {\bf 45}, 974 (1992), E {\bf 49}, 501, (1994)) the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalised spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self- consistently. We estimate the value of elastic constants using reasonable guess for the order and structural- parameters.Comment: 31 pages; 1 Fig. in GIF format, To be appear in Phys. Rev.

Theory and simulation of the nematic zenithal anchoring coefficient

Combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the zenithal surface anchoring coefficient on the value of the bulk order parameter

Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order is rapidly decaying when moving away from the surface, the uniaxial nematic order parameter shows an oscillatory behavior close to the substrate, accompanied by a non-zero local biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure

Liquid crystal director fluctuations and surface anchoring by molecular simulation

We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length

Elastic constants of hard and soft nematic liquid crystals

The Frank elastic constants for a nematic liquid crystal have been calculated by computer simulations for a fluid of hard ellipsoids and by the Poniewierski-Stecki method for ellipsoids with and without an attractive square well. Required for the Poniewierski-Stecki method is the direct correlation function c(1,2) and its dependence on the mutual molecular orientations. This was addressed using several models: the Parsons model, a two-term virial expansion, and the PY and HNC theories of Patey et al. In the Parsons model for c(1,2), the derived Frank elastic constants for hard ellipsoids were in agreement with the Poniewierski-Holyst values for hard spherocylinders. However, the agreement with simulation values was less satisfactory, as the simulation values exceeded the Parsons model values and the discrepancy grew with increasing particle asymmetry. The Frank constants, derived using a hard-core potential with an exterior SW (convex peg in a round hole), were in fair agreement with experimental data on prolate and oblate molecules, at the expense of employing overly large-order parameters (characteristic of uniaxial hard particle models). Omitted long-range correlations in the c( 1,2), present even in the hard-body models, is suspected to be the cause of the discrepancy of the simulation and experimental Frank constants with those calculated on the basis of short-range models for c(1,2)